Edit Profile (opens in new tab) Houston, Paul Compute Distance To: Compute Author ID: houston.paul Published as: Houston, Paul; Houston, P. External Links: MGP Documents Indexed: 98 Publications since 1997, including 1 Book Co-Authors: 56 Co-Authors with 95 Joint Publications 1,659 Co-Co-Authors all top 5 Co-Authors 1 single-authored 21 Süli, Endre E. 14 Schötzau, Dominik 14 Wihler, Thomas Pascal 10 Antonietti, Paola Francesca 10 Hall, Edward J. C. 10 Perugia, Ilaria 9 Georgoulis, Emmanuil H. 8 Cliffe, K. Andrew 8 Giani, Stefano 8 Hartmann, Ralf 7 Congreve, Scott 4 Cangiani, Andrea 4 Schwab, Christoph 4 van der Zee, Kristoffer George 3 Collis, Joe 3 Dong, Zhaonan 3 Pennesi, Giorgio 3 Phipps, Eric T. 3 Roggendorf, Sarah 3 Salinger, Andrew G. 3 Schneebeli, Anna 3 Senior, Bill 2 Verani, Marco 1 Bain, Oliver 1 Billingham, John 1 Brezzi, Franco 1 Brownlee, Robert 1 Buffa, Annalisa 1 Facciolà, Chiara 1 Gavaghan, David J. 1 Harriman, Kathryn 1 Holton, Derek Allan 1 Hu, Xiaozhe 1 Jackson, C. P. 1 Jensen, Max 1 Joyce, Simon 1 Levesley, Jeremy 1 Lowndes, Ian S. 1 Maini, Philip Kumar 1 Marini, Luisa Donatella 1 Mazzieri, Ilario 1 McInerney, Darragh 1 Monk, Nicholas A. M. 1 Muga, Ignacio 1 Murphy, Steven 1 Owen, Markus Roger 1 Pasquale, Liliana 1 Rannacher, Rolf 1 Robson, Janice 1 Rosswog, Stephan 1 Rourke, Connor J. 1 Sarti, Marco 1 Schamberg, S. 1 Sime, Nathan 1 Smears, Iain 1 Virtanen, Juha M. 1 Ward, Michael J. 1 Warnecke, Gerald G. 1 Wei, Xiaoxi 1 Zanchetta, Pericle 1 Zhu, Liang all top 5 Serials 10 Journal of Scientific Computing 9 SIAM Journal on Scientific Computing 8 International Journal of Numerical Analysis and Modeling 7 IMA Journal of Numerical Analysis 5 Computer Methods in Applied Mechanics and Engineering 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Computers & Mathematics with Applications 3 Mathematics of Computation 3 SIAM Journal on Numerical Analysis 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Computational Physics 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 2 Advances in Computational Mathematics 1 International Journal for Numerical Methods in Fluids 1 Journal of Engineering Mathematics 1 Bulletin of Mathematical Biology 1 Calcolo 1 Computing 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Applied Mathematics 1 Computational Methods in Applied Mathematics 1 Communications in Computational Physics 1 Numerical Mathematics: Theory, Methods and Applications 1 International Journal of Computing Science and Mathematics 1 SpringerBriefs in Mathematics all top 5 Fields 83 Numerical analysis (65-XX) 48 Partial differential equations (35-XX) 32 Fluid mechanics (76-XX) 10 Optics, electromagnetic theory (78-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of deformable solids (74-XX) 2 Approximations and expansions (41-XX) 2 Geophysics (86-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 91 Publications have been cited 2,194 times in 1,273 Documents Cited by ▼ Year ▼ Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067Houston, Paul; Schwab, Christoph; Süli, Endre 218 2002 Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Zbl 1057.76033Hartmann, Ralf; Houston, Paul 98 2002 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1298.65167Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul 93 2014 Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Zbl 1034.65081Hartmann, Ralf; Houston, Paul 76 2002 A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. Zbl 1074.65131Houston, Paul; Süli, Endre 75 2005 Energy norm a posteriori error estimation of \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems. Zbl 1116.65115Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 73 2007 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1382.65307Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 66 2017 Interior penalty method for the indefinite time-harmonic Maxwell equations. Zbl 1071.65155Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 58 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator. Zbl 1084.65115Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 57 2004 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103Houston, Paul; Schwab, Christoph; Süli, Endre 55 2000 An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Zbl 1359.76220Hartmann, Ralf; Houston, Paul 55 2008 \(hp\)-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1284.65163Antonietti, Paola F.; Giani, Stefano; Houston, Paul 52 2013 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. Zbl 1129.76030Hartmann, Ralf; Houston, Paul 48 2006 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Zbl 1084.65116Houston, Paul; Robson, Janice; Süli, Endre 47 2005 Discontinuous Galerkin methods for the biharmonic problem. Zbl 1176.65134Georgoulis, Emmanuil H.; Houston, Paul 43 2009 \(hp\)-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. Zbl 1029.65130Houston, Paul; Endre Süli 41 2001 A posteriori error analysis for numerical approximations of Friedrichs systems. Zbl 0935.65096Houston, Paul; Mackenzie, J. A.; Süli, Endre; Warnecke, Gerald 38 1999 \(hp\)-version discontinous Gelerkin methods for advection-diffusion-reaction problems on polytropic meshes. Zbl 1342.65213Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 35 2016 Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. Zbl 1357.65251Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul 34 2016 A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods. Zbl 1230.65123Antonietti, Paola F.; Houston, Paul 34 2011 Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. Zbl 1159.65092Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 33 2007 An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems. Zbl 1209.65124Georgoulis, Emmanuil H.; Houston, Paul; Virtanen, Juha 32 2011 Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. Zbl 1131.78007Buffa, Annalisa; Houston, Paul; Perugia, Ilaria 31 2007 Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems. Zbl 0957.65085Houston, Paul; Süli, Endre 30 2001 An \(hp\)-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity. Zbl 1118.74049Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 30 2006 A posteriori error analysis of \(hp\)-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs. Zbl 1144.65070Houston, Paul; Süli, Endre; Wihler, Thomas P. 28 2008 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. Zbl 1063.78021Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 27 2005 Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. Zbl 1211.37094Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul 27 2010 A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115Houston, Paul; Rannacher, Rolf; Süli, Endre 26 2000 \(hp\)-discontinuous Galerkin finite element methods for hyperbolic problems: Error analysis and adaptivity. Zbl 1021.76027Houston, Paul; Senior, Bill; Süli, Endre 26 2002 Stabilised \(hp\)-finite element approximation of partial differential equations with nonnegative characteristic form. Zbl 0985.65136Houston, P.; Süli, E. 25 2001 Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1421.65029Antonietti, Paola F.; Houston, Paul; Hu, Xiaozhe; Sarti, Marco; Verani, Marco 24 2017 A mixed DG method for linearized incompressible magnetohydrodynamics. Zbl 1203.76083Houston, Paul; Schötzau, Dominik; Wei, Xiaoxi 24 2009 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. II. Goal-oriented a posteriori error estimation. Zbl 1152.76429Hartmann, Ralf; Houston, Paul 23 2006 Energy norm a posteriori error estimation for \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Zbl 1220.65156Zhu, Liang; Giani, Stefano; Houston, Paul; Schötzau, Dominik 23 2011 Sobolev regularity estimation for \(hp\)-adaptive finite element methods. Zbl 1043.65114Houston, P.; Senior, B.; Süli, E. 22 2003 \(hp\)-version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. Zbl 1037.65117Harriman, Kathryn; Houston, Paul; Senior, Bill; Süli, Endre 20 2003 Modeling subgrid viscosity for advection-diffusion problems. Zbl 0980.76042Brezzi, F.; Houston, P.; Marini, D.; Süli, E. 20 2000 Adaptive finite element approximation of hyperbolic problems. Zbl 1141.76428Süli, Endre; Houston, Paul 20 2003 Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. Zbl 1091.78017Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 19 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. Zbl 1065.76139Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 19 2005 \(hp\)-DGFEM for partial differential equations with nonnegative characteristic form. Zbl 0946.65102Süli, Endre; Schwab, Christoph; Houston, Paul 19 2000 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity. Zbl 1175.65127Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 19 2009 Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1307.65174Antonietti, Paola F.; Giani, Stefano; Houston, Paul 17 2014 Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods. Zbl 1435.65044Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio 15 2018 The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip 15 2002 Finite element methods for hyperbolic problems: A posteriori error analysis and adaptivity. Zbl 0886.65104Süli, Endre; Houston, Paul 15 1997 An a posteriori error indicator for discontinuous Galerkin discretizations of \(H\)(curl)-elliptic partial differential equations. Zbl 1148.65088Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 14 2007 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Zbl 1279.65132Congreve, Scott; Houston, Paul; Wihler, Thomas P. 14 2013 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. I: A priori error analysis. Zbl 1185.65208Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 12 2007 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems. II: Strongly monotone quasi-Newtonian flows. Zbl 1457.65192Congreve, Scott; Houston, Paul; Süli, Endre; Wihler, Thomas P. 12 2013 A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for \(hp\)-version discontinuous Galerkin methods. Zbl 1350.65134Antonietti, Paola F.; Houston, Paul; Smears, Iain 11 2016 Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. Zbl 1087.65106Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 11 2005 \(hp\)-finite element methods for hyperbolic problems. Zbl 0959.65127Süli, Endre; Houston, Paul; Schwab, Christoph 11 2000 \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1298.65173Giani, Stefano; Houston, Paul 11 2014 An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Zbl 1442.65422Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio; Süli, Endre 11 2020 \(hp\)-DGFEM for Maxwell’s equations. Zbl 1061.78012Houston, P.; Perugia, I.; Schötzau, D. 10 2003 Goal-oriented a posteriori error estimation for multiple target functionals. Zbl 1064.65102Hartmann, Ralf; Houston, Paul 10 2003 \(hp\)-discontinuous Galerkin finite element methods with least-squares stabilization. Zbl 1053.76040Houston, Paul; Jensen, Max; Süli, Endre 10 2002 Anisotropic \(hp\)-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Zbl 1263.76042Giani, Stefano; Houston, Paul 10 2012 Mixed \(hp\)-discontinuous Galerkin finite element methods for the Stokes problem in polygons. Zbl 1179.76053Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 10 2004 Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Zbl 1329.76170Giani, S.; Houston, P. 9 2014 An \(hp\)-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Zbl 1410.65449Houston, Paul; Wihler, Thomas P. 9 2018 Adaptivity and a posteriori error control for bifurcation problems. I: The Bratu problem. Zbl 1364.65246Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 7 2010 High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations. Zbl 1470.86002Antonietti, Paola F.; Facciolà, Chiara; Houston, Paul; Mazzieri, Ilario; Pennesi, Giorgio; Verani, Marco 6 2021 Goal-oriented a posteriori error estimation for compressible fluid flows. Zbl 1042.76042Hartmann, R.; Houston, P. 6 2003 Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry. Zbl 1311.76053Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 6 2012 The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin’s method. Zbl 1429.35070Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer G. 6 2019 Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation. Zbl 1447.65146Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 6 2020 Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. Zbl 1320.76066Cliffe, K. A.; Collis, J.; Houston, P. 5 2015 Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. Zbl 1311.76052Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 5 2011 Discontinuous Galerkin methods for problems with Dirac delta source. Zbl 1272.65092Houston, Paul; Wihler, Thomas Pascal 5 2012 \(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Zbl 1381.76157Cliffe, K. A.; Hall, E. J. C.; Houston, P. 4 2014 Adaptive discontinuous Galerkin methods on polytopic meshes. Zbl 1371.74258Collis, Joe; Houston, Paul 4 2016 \(hp\)-adaptive discontinuous Galerkin methods for neutron transport criticality problems. Zbl 1385.82001Hall, Edward; Houston, Paul; Murphy, Steven 4 2017 Domain decomposition preconditioners for discontinuous Galerkin discretization of compressible fluid flows. Zbl 1324.76031Giani, Stefano; Houston, Paul 4 2014 Automatic symbolic computation for discontinuous Galerkin finite element methods. Zbl 1397.65268Houston, Paul; Sime, Nathan 4 2018 A pre-processing moving mesh method for discontinuous Galerkin approximations of advection-diffusion-reaction problems. Zbl 1162.65403Antonietti, Paola F.; Houston, Paul 4 2008 Adjoint error estimation and adaptivity for hyperbolic problems. Zbl 1368.65164Houston, P. 3 2017 Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Zbl 1419.65105Congreve, Scott; Houston, Paul; Perugia, Ilaria 3 2019 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1499.65651Congreve, Scott; Houston, Paul 3 2014 Adaptive energy minimisation for \(hp\)-finite element methods. Zbl 1443.65335Houston, Paul; Wihler, Thomas P. 2 2016 Two-grid \(hp\)-DGFEM for second-order quasilinear elliptic PDEs based on an incomplete Newton iteration. Zbl 1280.65124Congreve, Scott; Houston, Paul 2 2013 Gibbs phenomena for \(L^q\)-best approximation in finite element spaces. Zbl 1483.65188Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 2 2022 Output feedback control of flow separation over an aerofoil using plasma actuators. Zbl 1409.93027Broglia, R.; Choi, K.-S.; Houston, P.; Pasquale, L.; Zanchetta, P. 1 2018 Conditioning discrete fracture network models of groundwater flow. Zbl 1426.76238Cliffe, K.; Holton, D.; Houston, P.; Jackson, C.; Joyce, S.; Milne, A. 1 2011 Adaptive discontinuous Galerkin finite element methods with interior penalty for the compressible Navier-Stokes equations. Zbl 1179.76051Hartmann, Ralf; Houston, Paul 1 2004 Second-order elliptic PDEs with discontinuous boundary data. Zbl 1237.65124Houston, Paul; Wihler, Thomas P. 1 2012 Application of \(hp\)-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. Zbl 1273.76267Cliffe, K. A.; Hall, E. J. C.; Houston, P. 1 2013 \(hp\)-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1273.76268Congreve, S.; Houston, P.; Wihler, T. P. 1 2013 Linearization of the travel time functional in porous media flows. Zbl 1490.65198Houston, Paul; Rourke, Connor J.; van der Zee, Kristoffer G. 1 2022 Gibbs phenomena for \(L^q\)-best approximation in finite element spaces. Zbl 1483.65188Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 2 2022 Linearization of the travel time functional in porous media flows. Zbl 1490.65198Houston, Paul; Rourke, Connor J.; van der Zee, Kristoffer G. 1 2022 High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations. Zbl 1470.86002Antonietti, Paola F.; Facciolà, Chiara; Houston, Paul; Mazzieri, Ilario; Pennesi, Giorgio; Verani, Marco 6 2021 An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Zbl 1442.65422Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio; Süli, Endre 11 2020 Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation. Zbl 1447.65146Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 6 2020 The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin’s method. Zbl 1429.35070Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer G. 6 2019 Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Zbl 1419.65105Congreve, Scott; Houston, Paul; Perugia, Ilaria 3 2019 Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods. Zbl 1435.65044Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio 15 2018 An \(hp\)-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Zbl 1410.65449Houston, Paul; Wihler, Thomas P. 9 2018 Automatic symbolic computation for discontinuous Galerkin finite element methods. Zbl 1397.65268Houston, Paul; Sime, Nathan 4 2018 Output feedback control of flow separation over an aerofoil using plasma actuators. Zbl 1409.93027Broglia, R.; Choi, K.-S.; Houston, P.; Pasquale, L.; Zanchetta, P. 1 2018 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1382.65307Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 66 2017 Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1421.65029Antonietti, Paola F.; Houston, Paul; Hu, Xiaozhe; Sarti, Marco; Verani, Marco 24 2017 \(hp\)-adaptive discontinuous Galerkin methods for neutron transport criticality problems. Zbl 1385.82001Hall, Edward; Houston, Paul; Murphy, Steven 4 2017 Adjoint error estimation and adaptivity for hyperbolic problems. Zbl 1368.65164Houston, P. 3 2017 \(hp\)-version discontinous Gelerkin methods for advection-diffusion-reaction problems on polytropic meshes. Zbl 1342.65213Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 35 2016 Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. Zbl 1357.65251Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul 34 2016 A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for \(hp\)-version discontinuous Galerkin methods. Zbl 1350.65134Antonietti, Paola F.; Houston, Paul; Smears, Iain 11 2016 Adaptive discontinuous Galerkin methods on polytopic meshes. Zbl 1371.74258Collis, Joe; Houston, Paul 4 2016 Adaptive energy minimisation for \(hp\)-finite element methods. Zbl 1443.65335Houston, Paul; Wihler, Thomas P. 2 2016 Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. Zbl 1320.76066Cliffe, K. A.; Collis, J.; Houston, P. 5 2015 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1298.65167Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul 93 2014 Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1307.65174Antonietti, Paola F.; Giani, Stefano; Houston, Paul 17 2014 \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1298.65173Giani, Stefano; Houston, Paul 11 2014 Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Zbl 1329.76170Giani, S.; Houston, P. 9 2014 \(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Zbl 1381.76157Cliffe, K. A.; Hall, E. J. C.; Houston, P. 4 2014 Domain decomposition preconditioners for discontinuous Galerkin discretization of compressible fluid flows. Zbl 1324.76031Giani, Stefano; Houston, Paul 4 2014 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1499.65651Congreve, Scott; Houston, Paul 3 2014 \(hp\)-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1284.65163Antonietti, Paola F.; Giani, Stefano; Houston, Paul 52 2013 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Zbl 1279.65132Congreve, Scott; Houston, Paul; Wihler, Thomas P. 14 2013 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems. II: Strongly monotone quasi-Newtonian flows. Zbl 1457.65192Congreve, Scott; Houston, Paul; Süli, Endre; Wihler, Thomas P. 12 2013 Two-grid \(hp\)-DGFEM for second-order quasilinear elliptic PDEs based on an incomplete Newton iteration. Zbl 1280.65124Congreve, Scott; Houston, Paul 2 2013 Application of \(hp\)-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. Zbl 1273.76267Cliffe, K. A.; Hall, E. J. C.; Houston, P. 1 2013 \(hp\)-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1273.76268Congreve, S.; Houston, P.; Wihler, T. P. 1 2013 Anisotropic \(hp\)-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Zbl 1263.76042Giani, Stefano; Houston, Paul 10 2012 Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry. Zbl 1311.76053Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 6 2012 Discontinuous Galerkin methods for problems with Dirac delta source. Zbl 1272.65092Houston, Paul; Wihler, Thomas Pascal 5 2012 Second-order elliptic PDEs with discontinuous boundary data. Zbl 1237.65124Houston, Paul; Wihler, Thomas P. 1 2012 A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods. Zbl 1230.65123Antonietti, Paola F.; Houston, Paul 34 2011 An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems. Zbl 1209.65124Georgoulis, Emmanuil H.; Houston, Paul; Virtanen, Juha 32 2011 Energy norm a posteriori error estimation for \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Zbl 1220.65156Zhu, Liang; Giani, Stefano; Houston, Paul; Schötzau, Dominik 23 2011 Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. Zbl 1311.76052Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 5 2011 Conditioning discrete fracture network models of groundwater flow. Zbl 1426.76238Cliffe, K.; Holton, D.; Houston, P.; Jackson, C.; Joyce, S.; Milne, A. 1 2011 Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. Zbl 1211.37094Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul 27 2010 Adaptivity and a posteriori error control for bifurcation problems. I: The Bratu problem. Zbl 1364.65246Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 7 2010 Discontinuous Galerkin methods for the biharmonic problem. Zbl 1176.65134Georgoulis, Emmanuil H.; Houston, Paul 43 2009 A mixed DG method for linearized incompressible magnetohydrodynamics. Zbl 1203.76083Houston, Paul; Schötzau, Dominik; Wei, Xiaoxi 24 2009 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity. Zbl 1175.65127Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 19 2009 An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Zbl 1359.76220Hartmann, Ralf; Houston, Paul 55 2008 A posteriori error analysis of \(hp\)-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs. Zbl 1144.65070Houston, Paul; Süli, Endre; Wihler, Thomas P. 28 2008 A pre-processing moving mesh method for discontinuous Galerkin approximations of advection-diffusion-reaction problems. Zbl 1162.65403Antonietti, Paola F.; Houston, Paul 4 2008 Energy norm a posteriori error estimation of \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems. Zbl 1116.65115Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 73 2007 Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. Zbl 1159.65092Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 33 2007 Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. Zbl 1131.78007Buffa, Annalisa; Houston, Paul; Perugia, Ilaria 31 2007 An a posteriori error indicator for discontinuous Galerkin discretizations of \(H\)(curl)-elliptic partial differential equations. Zbl 1148.65088Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 14 2007 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. I: A priori error analysis. Zbl 1185.65208Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 12 2007 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. Zbl 1129.76030Hartmann, Ralf; Houston, Paul 48 2006 An \(hp\)-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity. Zbl 1118.74049Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 30 2006 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. II. Goal-oriented a posteriori error estimation. Zbl 1152.76429Hartmann, Ralf; Houston, Paul 23 2006 A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. Zbl 1074.65131Houston, Paul; Süli, Endre 75 2005 Interior penalty method for the indefinite time-harmonic Maxwell equations. Zbl 1071.65155Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 58 2005 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Zbl 1084.65116Houston, Paul; Robson, Janice; Süli, Endre 47 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. Zbl 1063.78021Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 27 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. Zbl 1091.78017Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 19 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. Zbl 1065.76139Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 19 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. Zbl 1087.65106Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 11 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator. Zbl 1084.65115Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 57 2004 Mixed \(hp\)-discontinuous Galerkin finite element methods for the Stokes problem in polygons. Zbl 1179.76053Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 10 2004 Adaptive discontinuous Galerkin finite element methods with interior penalty for the compressible Navier-Stokes equations. Zbl 1179.76051Hartmann, Ralf; Houston, Paul 1 2004 Sobolev regularity estimation for \(hp\)-adaptive finite element methods. Zbl 1043.65114Houston, P.; Senior, B.; Süli, E. 22 2003 \(hp\)-version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. Zbl 1037.65117Harriman, Kathryn; Houston, Paul; Senior, Bill; Süli, Endre 20 2003 Adaptive finite element approximation of hyperbolic problems. Zbl 1141.76428Süli, Endre; Houston, Paul 20 2003 \(hp\)-DGFEM for Maxwell’s equations. Zbl 1061.78012Houston, P.; Perugia, I.; Schötzau, D. 10 2003 Goal-oriented a posteriori error estimation for multiple target functionals. Zbl 1064.65102Hartmann, Ralf; Houston, Paul 10 2003 Goal-oriented a posteriori error estimation for compressible fluid flows. Zbl 1042.76042Hartmann, R.; Houston, P. 6 2003 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067Houston, Paul; Schwab, Christoph; Süli, Endre 218 2002 Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Zbl 1057.76033Hartmann, Ralf; Houston, Paul 98 2002 Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Zbl 1034.65081Hartmann, Ralf; Houston, Paul 76 2002 \(hp\)-discontinuous Galerkin finite element methods for hyperbolic problems: Error analysis and adaptivity. Zbl 1021.76027Houston, Paul; Senior, Bill; Süli, Endre 26 2002 The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip 15 2002 \(hp\)-discontinuous Galerkin finite element methods with least-squares stabilization. Zbl 1053.76040Houston, Paul; Jensen, Max; Süli, Endre 10 2002 \(hp\)-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. Zbl 1029.65130Houston, Paul; Endre Süli 41 2001 Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems. Zbl 0957.65085Houston, Paul; Süli, Endre 30 2001 Stabilised \(hp\)-finite element approximation of partial differential equations with nonnegative characteristic form. Zbl 0985.65136Houston, P.; Süli, E. 25 2001 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103Houston, Paul; Schwab, Christoph; Süli, Endre 55 2000 A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115Houston, Paul; Rannacher, Rolf; Süli, Endre 26 2000 Modeling subgrid viscosity for advection-diffusion problems. Zbl 0980.76042Brezzi, F.; Houston, P.; Marini, D.; Süli, E. 20 2000 \(hp\)-DGFEM for partial differential equations with nonnegative characteristic form. Zbl 0946.65102Süli, Endre; Schwab, Christoph; Houston, Paul 19 2000 \(hp\)-finite element methods for hyperbolic problems. Zbl 0959.65127Süli, Endre; Houston, Paul; Schwab, Christoph 11 2000 A posteriori error analysis for numerical approximations of Friedrichs systems. Zbl 0935.65096Houston, Paul; Mackenzie, J. A.; Süli, Endre; Warnecke, Gerald 38 1999 Finite element methods for hyperbolic problems: A posteriori error analysis and adaptivity. Zbl 0886.65104Süli, Endre; Houston, Paul 15 1997 all cited Publications top 5 cited Publications all top 5 Cited by 1,635 Authors 43 Houston, Paul 42 Antonietti, Paola Francesca 28 Li, Jichun 27 Giani, Stefano 25 Dolejší, Vít 25 Schötzau, Dominik 21 Georgoulis, Emmanuil H. 21 Wihler, Thomas Pascal 19 Verani, Marco 16 Dumbser, Michael 15 Ern, Alexandre 15 Perugia, Ilaria 14 Huang, Yunqing 14 Liu, Tiegang 13 Di Pietro, Daniele Antonio 13 Feistauer, Miloslav 13 Gudi, Thirupathi 12 Beirão da Veiga, Lourenço 12 Cangiani, Andrea 12 Mazzieri, Ilario 12 Süli, Endre E. 11 Fidkowski, Krzysztof J. 11 Mascotto, Lorenzo 11 Schwab, Christoph 10 Adjerid, Slimane 10 Baccouch, Mahboub 10 Cockburn, Bernardo 10 Dong, Zhaonan 10 Nataraj, Neela 10 Pryer, Tristan 9 Banz, Lothar 9 Burman, Erik 9 Cheng, Jian 9 Chung, Tsz Shun Eric 9 Demkowicz, Leszek F. 9 Stamm, Benjamin 8 Manzini, Gianmarco 8 Mora, David 8 Park, Eun-Jae 8 Rui, Hongxing 8 Vohralík, Martin 8 Wheeler, Mary Fanett 8 Yang, Wei 8 Ye, Xiu 7 Bertoluzza, Silvia 7 Bi, Chunjia 7 Brenner, Susanne Cecelia 7 Carstensen, Carsten 7 Dedner, Andreas S. 7 Giesselmann, Jan 7 Hall, Edward J. C. 7 Hiptmair, Ralf 7 May, Georg 7 Mu, Lin 7 Quarteroni, Alfio M. 7 Rivera, Gonzalo 7 Schroder, Andreas 7 Tavener, Simon J. 7 van der Vegt, Jaap J. W. 7 Wei, Juncheng 7 Zhang, Shangyou 7 Zhao, Lina 6 Abdulle, Assyr 6 Badia, Santiago 6 Botti, Lorenzo 6 Brezzi, Franco 6 Darmofal, David L. 6 Endtmayer, Bernhard 6 Fu, Hongfei 6 Gassner, Gregor J. 6 Gatica, Gabriel N. 6 Hartmann, Ralf 6 He, Yinnian 6 Hoppe, Ronald H. W. 6 Huang, Xuehai 6 Kuzmin, Dmitri 6 Lube, Gert 6 Marini, Luisa Donatella 6 Müller, Siegfried 6 Munz, Claus-Dieter 6 Nicaise, Serge 6 Pani, Amiya Kumar 6 Prada, Daniele 6 Rivière, Beatrice M. 6 Russo, Alessandro 6 Takizawa, Kenji 6 Tezduyar, Tayfun E. 6 van der Zee, Kristoffer George 6 Wick, Thomas 6 Yue, Huiqiang 6 Zhang, Zhimin 6 Zhong, Liuqiang 6 Zhu, Hongqiang 5 Bastian, Peter 5 Botti, Michele 5 Bustinza, Rommel A. 5 Chapelier, Jean-Baptiste 5 Chernov, Alexey 5 Codina, Ramon 5 de la Llave Plata, Marta ...and 1,535 more Authors all top 5 Cited in 142 Serials 150 Journal of Computational Physics 111 Journal of Scientific Computing 107 Computer Methods in Applied Mechanics and Engineering 83 Computers & Mathematics with Applications 68 Journal of Computational and Applied Mathematics 57 Applied Numerical Mathematics 49 Mathematics of Computation 46 Computers and Fluids 42 Numerische Mathematik 42 SIAM Journal on Scientific Computing 35 Applied Mathematics and Computation 34 SIAM Journal on Numerical Analysis 31 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 30 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 28 Numerical Methods for Partial Differential Equations 17 Advances in Computational Mathematics 14 Communications in Computational Physics 13 Calcolo 13 Computational Methods in Applied Mathematics 13 Journal of Numerical Mathematics 12 Computational Mechanics 11 Communications on Applied Mathematics and Computation 10 International Journal for Numerical Methods in Fluids 10 BIT 9 International Journal of Numerical Analysis and Modeling 8 International Journal for Numerical Methods in Engineering 8 Mathematics and Computers in Simulation 7 Advances in Applied Mathematics and Mechanics 6 Numerical Algorithms 6 International Journal of Computer Mathematics 6 Engineering Analysis with Boundary Elements 6 Computational Geosciences 5 Numerical Functional Analysis and Optimization 5 Foundations of Computational Mathematics 4 Applied Mathematics Letters 4 Applications of Mathematics 4 East Asian Journal on Applied Mathematics 4 Results in Applied Mathematics 3 Applicable Analysis 3 Computer Physics Communications 3 Journal of Differential Equations 3 Computational Optimization and Applications 3 Numerical Linear Algebra with Applications 3 Mathematical Problems in Engineering 3 Computing and Visualization in Science 3 International Journal of Computational Fluid Dynamics 3 Archives of Computational Methods in Engineering 3 Multiscale Modeling & Simulation 3 International Journal for Numerical Methods in Biomedical Engineering 2 Mathematical Methods in the Applied Sciences 2 Bulletin of Mathematical Biology 2 Meccanica 2 Physica D 2 COMPEL 2 European Journal of Applied Mathematics 2 Communications in Partial Differential Equations 2 Journal of Nonlinear Science 2 Communications in Numerical Methods in Engineering 2 Vietnam Journal of Mathematics 2 Abstract and Applied Analysis 2 International Journal of Theoretical and Applied Finance 2 Communications in Nonlinear Science and Numerical Simulation 2 Central European Journal of Mathematics 2 International Journal of Computational Methods 2 Advances in Difference Equations 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Computational and Theoretical Transport 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 ACM Transactions on Mathematical Software 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 Acta Applicandae Mathematicae 1 Computer Aided Geometric Design 1 Journal of Computational Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Journal of Dynamics and Differential Equations 1 Advances in Engineering Software 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Journal of Difference Equations and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Inequalities and Applications 1 European Journal of Mechanics. B. Fluids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Engineering Computations 1 Combustion Theory and Modelling 1 Lobachevskii Journal of Mathematics 1 The ANZIAM Journal 1 Matematicheskoe Modelirovanie ...and 42 more Serials all top 5 Cited in 37 Fields 1,117 Numerical analysis (65-XX) 579 Partial differential equations (35-XX) 383 Fluid mechanics (76-XX) 120 Mechanics of deformable solids (74-XX) 119 Optics, electromagnetic theory (78-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 23 Biology and other natural sciences (92-XX) 18 Statistical mechanics, structure of matter (82-XX) 14 Classical thermodynamics, heat transfer (80-XX) 13 Ordinary differential equations (34-XX) 10 Integral equations (45-XX) 10 Geophysics (86-XX) 9 Functional analysis (46-XX) 8 Approximations and expansions (41-XX) 8 Operator theory (47-XX) 8 Computer science (68-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Potential theory (31-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 5 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Astronomy and astrophysics (85-XX) 3 Operations research, mathematical programming (90-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year