Badger, Jacob; Henneking, Stefan; Petrides, Socratis; Demkowicz, Leszek Scalable DPG multigrid solver for Helmholtz problems: a study on convergence. (English) Zbl 07750283 Comput. Math. Appl. 148, 81-92 (2023). MSC: 65N30 35J05 65N55 65F08 65F10 PDFBibTeX XMLCite \textit{J. Badger} et al., Comput. Math. Appl. 148, 81--92 (2023; Zbl 07750283) Full Text: DOI arXiv
Giani, Stefano; Engström, Christian; Grubišić, Luka \(khp\)-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory. (English) Zbl 07732712 J. Comput. Appl. Math. 429, Article ID 115212, 19 p. (2023). MSC: 65Nxx 35Pxx 65Rxx PDFBibTeX XMLCite \textit{S. Giani} et al., J. Comput. Appl. Math. 429, Article ID 115212, 19 p. (2023; Zbl 07732712) Full Text: DOI
Henneking, S.; Demkowicz, L. A numerical study of the pollution error and DPG adaptivity for long waveguide simulations. (English) Zbl 1524.65812 Comput. Math. Appl. 95, 85-100 (2021). MSC: 65N30 35J05 65N12 65N15 78A50 78A25 35Q60 65N50 65Y05 PDFBibTeX XMLCite \textit{S. Henneking} and \textit{L. Demkowicz}, Comput. Math. Appl. 95, 85--100 (2021; Zbl 1524.65812) Full Text: DOI arXiv
Petrides, Socratis; Demkowicz, Leszek An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics. (English) Zbl 1524.65927 Comput. Math. Appl. 87, 12-26 (2021). MSC: 65N55 65N30 35J05 65F10 65F08 65N50 76Q05 78A40 35Q60 76M10 78M10 35Q35 PDFBibTeX XMLCite \textit{S. Petrides} and \textit{L. Demkowicz}, Comput. Math. Appl. 87, 12--26 (2021; Zbl 1524.65927) Full Text: DOI arXiv
Giani, Stefano; Hakula, Harri On effective material parameters of thin perforated shells under static loading. (English) Zbl 1442.74120 Comput. Methods Appl. Mech. Eng. 367, Article ID 113094, 17 p. (2020). MSC: 74K25 74Q05 PDFBibTeX XMLCite \textit{S. Giani} and \textit{H. Hakula}, Comput. Methods Appl. Mech. Eng. 367, Article ID 113094, 17 p. (2020; Zbl 1442.74120) Full Text: DOI Link
Bériot, Hadrien; Gabard, Gwénaël Anisotropic adaptivity of the \(p\)-FEM for time-harmonic acoustic wave propagation. (English) Zbl 1416.76096 J. Comput. Phys. 378, 234-256 (2019). MSC: 76M10 76Q05 65M60 PDFBibTeX XMLCite \textit{H. Bériot} and \textit{G. Gabard}, J. Comput. Phys. 378, 234--256 (2019; Zbl 1416.76096) Full Text: DOI
Hintermüller, Michael; Hinze, Michael; Kahle, Christian; Keil, Tobias A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn-Hilliard-Navier-Stokes system. (English) Zbl 1507.49027 Optim. Eng. 19, No. 3, 629-662 (2018). MSC: 49M25 65M60 76D05 PDFBibTeX XMLCite \textit{M. Hintermüller} et al., Optim. Eng. 19, No. 3, 629--662 (2018; Zbl 1507.49027) Full Text: DOI
Giani, Stefano \(HP\)-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems. (English) Zbl 1402.65157 SIAM J. Sci. Comput. 40, No. 5, B1391-B1418 (2018). MSC: 65N30 65N50 49M15 35J15 PDFBibTeX XMLCite \textit{S. Giani}, SIAM J. Sci. Comput. 40, No. 5, B1391--B1418 (2018; Zbl 1402.65157) Full Text: DOI
Houston, Paul; Wihler, Thomas P. An \(hp\)-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. (English) Zbl 1410.65449 Math. Comput. 87, No. 314, 2641-2674 (2018). Reviewer: Konstantinos Chrysafinos (Athens) MSC: 65N30 35J61 35J25 65H10 PDFBibTeX XMLCite \textit{P. Houston} and \textit{T. P. Wihler}, Math. Comput. 87, No. 314, 2641--2674 (2018; Zbl 1410.65449) Full Text: DOI arXiv
Łoś, M.; Schaefer, R.; Paszyński, M. Parallel space-time \(hp\) adaptive discretization scheme for parabolic problems. (English) Zbl 1462.65149 J. Comput. Appl. Math. 344, 819-835 (2018). MSC: 65M60 65M06 65N30 65N55 65N50 65M15 65Y05 PDFBibTeX XMLCite \textit{M. Łoś} et al., J. Comput. Appl. Math. 344, 819--835 (2018; Zbl 1462.65149) Full Text: DOI
Giani, Stefano Reliable anisotropic-adaptive discontinuous Galerkin method for simplified \(\mathbf{P}_{\mathbf{N}}\) approximations of radiative transfer. (English) Zbl 1448.65230 J. Comput. Appl. Math. 337, 225-243 (2018). MSC: 65N30 65N15 65N50 80A21 PDFBibTeX XMLCite \textit{S. Giani}, J. Comput. Appl. Math. 337, 225--243 (2018; Zbl 1448.65230) Full Text: DOI
Petrides, Socratis; Demkowicz, Leszek F. An adaptive DPG method for high frequency time-harmonic wave propagation problems. (English) Zbl 1397.65288 Comput. Math. Appl. 74, No. 8, 1999-2017 (2017). MSC: 65N30 65N55 65F08 65F10 PDFBibTeX XMLCite \textit{S. Petrides} and \textit{L. F. Demkowicz}, Comput. Math. Appl. 74, No. 8, 1999--2017 (2017; Zbl 1397.65288) Full Text: DOI
Houston, Paul; Wihler, Thomas P. Adaptive energy minimisation for \(hp\)-finite element methods. (English) Zbl 1443.65335 Comput. Math. Appl. 71, No. 4, 977-990 (2016). MSC: 65N30 65N35 PDFBibTeX XMLCite \textit{P. Houston} and \textit{T. P. Wihler}, Comput. Math. Appl. 71, No. 4, 977--990 (2016; Zbl 1443.65335) Full Text: DOI arXiv
Giani, Stefano; Seaid, Mohammed \(h p\)-adaptive discontinuous Galerkin methods for simplified \(\operatorname{P}_{\operatorname{N}}\) approximations of frequency-dependent radiative transfer. (English) Zbl 1425.74462 Comput. Methods Appl. Mech. Eng. 301, 52-79 (2016). MSC: 74S05 65N30 45K05 74A15 PDFBibTeX XMLCite \textit{S. Giani} and \textit{M. Seaid}, Comput. Methods Appl. Mech. Eng. 301, 52--79 (2016; Zbl 1425.74462) Full Text: DOI
Giani, Stefano \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains. (English) Zbl 1410.65436 Appl. Math. Comput. 267, 604-617 (2015). MSC: 65N25 35J25 35P05 65N30 PDFBibTeX XMLCite \textit{S. Giani}, Appl. Math. Comput. 267, 604--617 (2015; Zbl 1410.65436) Full Text: DOI
Congreve, Scott; Houston, Paul Two-grid \(hp\)-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. (English) Zbl 1499.65651 Int. J. Numer. Anal. Model. 11, No. 3, 496-524 (2014). MSC: 65N30 65N55 65N50 65H10 65N15 35J62 76A10 76M10 35Q35 PDFBibTeX XMLCite \textit{S. Congreve} and \textit{P. Houston}, Int. J. Numer. Anal. Model. 11, No. 3, 496--524 (2014; Zbl 1499.65651) Full Text: Link
Wixom, Andrew S.; McDaniel, J. Gregory Fast frequency sweeps with many forcing vectors through adaptive interpolatory model order reduction. (English) Zbl 1352.74449 Int. J. Numer. Methods Eng. 100, No. 6, 442-457 (2014). MSC: 74S05 70J50 65N30 74H45 PDFBibTeX XMLCite \textit{A. S. Wixom} and \textit{J. G. McDaniel}, Int. J. Numer. Methods Eng. 100, No. 6, 442--457 (2014; Zbl 1352.74449) Full Text: DOI
Giani, Stefano; Schötzau, Dominik; Zhu, Liang An a-posteriori error estimate for \(hp\)-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes. (English) Zbl 1350.65114 Comput. Math. Appl. 67, No. 4, 869-887 (2014). MSC: 65N15 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{S. Giani} et al., Comput. Math. Appl. 67, No. 4, 869--887 (2014; Zbl 1350.65114) Full Text: DOI
Cliffe, K. A.; Hall, E. J. C.; Houston, P. \(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. (English) Zbl 1381.76157 Comput. Math. Appl. 67, No. 4, 796-806 (2014). MSC: 76M10 37N10 65N30 37M20 76D05 PDFBibTeX XMLCite \textit{K. A. Cliffe} et al., Comput. Math. Appl. 67, No. 4, 796--806 (2014; Zbl 1381.76157) Full Text: DOI
Giani, Stefano; Houston, Paul \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. (English) Zbl 1298.65173 Numer. Methods Partial Differ. Equations 30, No. 4, 1342-1367 (2014). Reviewer: Marius Ghergu (Dublin) MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{S. Giani} and \textit{P. Houston}, Numer. Methods Partial Differ. Equations 30, No. 4, 1342--1367 (2014; Zbl 1298.65173) Full Text: DOI
Hetmaniuk, Ulrich; Tezaur, Radek; Farhat, Charbel An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems. (English) Zbl 1352.74132 Int. J. Numer. Methods Eng. 93, No. 10, 1109-1124 (2013). MSC: 74H15 65D05 74H45 76Q05 PDFBibTeX XMLCite \textit{U. Hetmaniuk} et al., Int. J. Numer. Methods Eng. 93, No. 10, 1109--1124 (2013; Zbl 1352.74132) Full Text: DOI
Giani, Stefano An a posteriori error estimator for \(hp\)-adaptive continuous Galerkin methods for photonic crystal applications. (English) Zbl 1311.78015 Computing 95, No. 5, 395-414 (2013). MSC: 78A60 65N25 65N30 65N50 65N15 78A40 78A50 PDFBibTeX XMLCite \textit{S. Giani}, Computing 95, No. 5, 395--414 (2013; Zbl 1311.78015) Full Text: DOI
Congreve, Scott; Houston, Paul; Wihler, Thomas P. Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. (English) Zbl 1279.65132 J. Sci. Comput. 55, No. 2, 471-497 (2013). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N30 65N15 35J62 PDFBibTeX XMLCite \textit{S. Congreve} et al., J. Sci. Comput. 55, No. 2, 471--497 (2013; Zbl 1279.65132) Full Text: DOI
Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry. (English) Zbl 1311.76053 J. Sci. Comput. 52, No. 1, 153-179 (2012). MSC: 76M10 65N30 65N15 76D05 PDFBibTeX XMLCite \textit{K. A. Cliffe} et al., J. Sci. Comput. 52, No. 1, 153--179 (2012; Zbl 1311.76053) Full Text: DOI
Rachowicz, W.; Zdunek, A. Application of the FEM with adaptivity for electromagnetic inverse medium scattering problems. (English) Zbl 1230.78017 Comput. Methods Appl. Mech. Eng. 200, No. 29-32, 2337-2347 (2011). MSC: 78A46 78M10 PDFBibTeX XMLCite \textit{W. Rachowicz} and \textit{A. Zdunek}, Comput. Methods Appl. Mech. Eng. 200, No. 29--32, 2337--2347 (2011; Zbl 1230.78017) Full Text: DOI
Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. (English) Zbl 1311.76052 J. Sci. Comput. 47, No. 3, 389-418 (2011). MSC: 76M10 65N30 65N15 76D05 PDFBibTeX XMLCite \textit{K. A. Cliffe} et al., J. Sci. Comput. 47, No. 3, 389--418 (2011; Zbl 1311.76052) Full Text: DOI
Pardo, David; Nam, Myung Jin; Torres-Verdín, Carlos; Hoversten, Michael G.; Garay, Iñaki Simulation of marine controlled source electromagnetic measurements using a parallel Fourier \(hp\)-finite element method. (English) Zbl 1209.86006 Comput. Geosci. 15, No. 1, 53-67 (2011). MSC: 86-08 76M12 PDFBibTeX XMLCite \textit{D. Pardo} et al., Comput. Geosci. 15, No. 1, 53--67 (2011; Zbl 1209.86006) Full Text: DOI
Paszyński, Maciej; Pardo, David; Torres-Verdín, Carlos; Demkowicz, Leszek; Calo, Victor A parallel direct solver for the self-adaptive \(hp\) finite element method. (English) Zbl 1233.68079 J. Parallel Distrib. Comput. 70, No. 3, 270-281 (2010). MSC: 68M14 PDFBibTeX XMLCite \textit{M. Paszyński} et al., J. Parallel Distrib. Comput. 70, No. 3, 270--281 (2010; Zbl 1233.68079) Full Text: DOI
Pardo, D.; Torres-Verdín, C.; Nam, M. J.; Paszynski, M.; Calo, V. M. Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D alternating current borehole resistivity measurements. (English) Zbl 1194.78068 Comput. Methods Appl. Mech. Eng. 197, No. 45-48, 3836-3849 (2008). MSC: 78M25 78M10 78A55 PDFBibTeX XMLCite \textit{D. Pardo} et al., Comput. Methods Appl. Mech. Eng. 197, No. 45--48, 3836--3849 (2008; Zbl 1194.78068) Full Text: DOI
Pardo, D.; Calo, V. M.; Torres-Verdín, C.; Nam, M. J. Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D-DC borehole resistivity measurements. (English) Zbl 1194.78067 Comput. Methods Appl. Mech. Eng. 197, No. 21-24, 1906-1925 (2008). MSC: 78M25 78M10 78A55 PDFBibTeX XMLCite \textit{D. Pardo} et al., Comput. Methods Appl. Mech. Eng. 197, No. 21--24, 1906--1925 (2008; Zbl 1194.78067) Full Text: DOI
Demkowicz, Leszek F.; Kurtz, Jason; Pardo, David; Paszyński, Maciej; Rachowicz, Waldemar; Zdunek, Adam Computing with \(hp\)-adaptive finite elements. Vol. II: Frontiers: Three-dimensional elliptic and Maxwell problems with applications. (English) Zbl 1148.65001 Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series. Boca Raton, FL: Chapman & Hall/CRC (ISBN 978-1-58488-672-3/hbk; 978-1-4200-1169-2/ebook). xv, 417 p. (2008). Reviewer: Georg Hebermehl (Berlin) MSC: 65-02 65N30 65N12 65N15 65N22 65N50 65Y05 78M10 74S05 76M10 78A46 PDFBibTeX XMLCite \textit{L. F. Demkowicz} et al., Computing with \(hp\)-adaptive finite elements. Vol. II: Frontiers: Three-dimensional elliptic and Maxwell problems with applications. Boca Raton, FL: Chapman \& Hall/CRC (2008; Zbl 1148.65001) Full Text: DOI
Paszyński, M.; Kurtz, J.; Demkowicz, L. Parallel, fully automatic \(hp\)-adaptive \(2d\) finite element package. (English) Zbl 1093.65113 Comput. Methods Appl. Mech. Eng. 195, No. 7-8, 711-741 (2006). MSC: 65N30 65N50 80A20 65Y05 78A45 78M10 80M10 35J05 PDFBibTeX XMLCite \textit{M. Paszyński} et al., Comput. Methods Appl. Mech. Eng. 195, No. 7--8, 711--741 (2006; Zbl 1093.65113) Full Text: DOI