Edit Profile (opens in new tab) Lie, Knut-Andreas Co-Author Distance Author ID: lie.knut-andreas Published as: Lie, Knut-Andreas; Lie, K.-A.; Lie, Knut Andreas; Lie, K.-a.; Lie, K. A. more...less External Links: MGP · ORCID Documents Indexed: 60 Publications since 1998, including 3 Books 3 Contributions as Editor Co-Authors: 68 Co-Authors with 59 Joint Publications 1,487 Co-Co-Authors all top 5 Co-Authors 4 single-authored 12 Møyner, Olav 11 Karlsen, Kenneth Hvistendahl 10 Nilsen, Halvor Møll 8 Natvig, Jostein Roald 7 Aarnes, Jørg E. 7 Krogstad, Stein 6 Holden, Helge 6 Risebro, Nils Henrik 5 Kippe, Vegard 5 Klemetsdal, Øystein Strengehagen 4 Andersen, Odd A. 4 Raynaud, Xavier 3 Hagen, Trond Runar 3 Noelle, Sebastian 3 Rasmussen, Atgeirr Flø 2 Bao, Kai 2 Brodtkorb, André Rigland 2 Dahle, Helge K. 2 Evje, Steinar 2 Ligaarden, Ingeborg Skjelkvåle 2 Moncorgé, Arthur 2 Mykkeltvedt, Trine S. 2 Rustad, Alf Birger 2 Skaflestad, Bard 2 Tai, Xuecheng 1 Allen, Rebecca 1 Berg, Carl Fredrik 1 Berge, Runar Lie 1 Berre, Inga 1 Blatt, Markus 1 Brusdal, Kari 1 Chan, Tony Fan-Cheong 1 Doster, Florian 1 Flemisch, Bernd 1 Ghaderi Zefreh, Masoud 1 Gimse, Tore 1 Haasdonk, Bernard 1 Hajibeygi, Hadi 1 Hasle, Geir 1 Haugse, V. 1 Henriksen, Martin Ofstad 1 Hjelmervik, Jon Mikkelsen 1 Holdahl, Runar 1 Hove, Joakim 1 Hvistendahl, K. 1 Kaulmann, Sven 1 Klöfkorn, Robert 1 Krotkiewski, Marcin 1 Lauser, Andreas 1 Linga, Gaute 1 Liu, Ming 1 Lysaker, Marius 1 Mørken, Knut M. 1 Nordhaug, Hans F. 1 Ohlberger, Mario 1 Osher, Stanley Joel 1 Quak, Ewald G. 1 Rosenbaum, Wolfram 1 Sætra, Martin L. 1 Sævareid, Ove 1 Sandve, Tor Harald 1 Schmid, Daniel W. 1 Shah, Swej 1 Ţene, Matei 1 Thune, Andreas 1 Watson, Francesca 1 Wu, Xiaohui 1 Yang, Yahan all top 5 Serials 22 Computational Geosciences 6 Journal of Computational Physics 2 BIT 2 Journal of Scientific Computing 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Engineering 1 Numerical Methods for Partial Differential Equations 1 Numerical Algorithms 1 SIAM Journal on Scientific Computing 1 Computing and Visualization in Science 1 Multiscale Modeling & Simulation 1 International Journal of Numerical Analysis and Modeling 1 Lecture Notes in Computer Science 1 Communications in Computational Physics 1 Mathematics and Visualization 1 EMS Series of Lectures in Mathematics 1 Journal of Computational Physics: X all top 5 Fields 45 Fluid mechanics (76-XX) 32 Numerical analysis (65-XX) 18 Partial differential equations (35-XX) 18 Geophysics (86-XX) 4 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 56 Publications have been cited 853 times in 639 Documents Cited by ▼ Year ▼ Open-source MATLAB implementation of consistent discretisations on complex grids. Zbl 1348.86002 Lie, Knut-Andreas; Krogstad, Stein; Ligaarden, Ingeborg Skjelkvåle; Natvig, Jostein Roald; Nilsen, Halvor Møll; Skaflestad, Bård 78 2012 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005 Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 75 2010 An introduction to reservoir simulation using MATLAB/GNU Octave. User guide for the MATLAB reservoir simulation toolbox (MRST). Zbl 1425.76001 Lie, Knut-Andreas 69 2019 On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. Zbl 1038.65078 Lie, Knut-Andreas; Noelle, Sebastian 67 2003 A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Zbl 1124.76022 Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas 55 2006 A comparison of multiscale methods for elliptic problems in porous media flow. Zbl 1259.76047 Kippe, Vegard; Aarnes, Jørg E.; Lie, Knut-Andreas 50 2008 A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. Zbl 1349.76824 Møyner, Olav; Lie, Knut-Andreas 44 2016 Multiscale mixed/mimetic methods on corner-point grids. Zbl 1259.76065 Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas 38 2008 An introduction to the numerics of flow in porous media using Matlab. Zbl 1330.76004 Aarnes, Jørg E.; Gimse, Tore; Lie, Knut-Andreas 24 2007 Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. Zbl 1051.76046 Karlsen, K. Hvistendahl; Lie, K.-A.; Natvig, J. R.; Nordhaug, H. F.; Dahle, H. K. 24 2001 Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. Zbl 1218.76029 Natvig, Jostein R.; Lie, Knut-Andreas 23 2008 An unconditionally stable splitting scheme for a class of nonlinear parabolic equations. Zbl 0949.65089 Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 22 1999 The corrected operator splitting approach applied to a nonlinear advection-diffusion problem. Zbl 0942.76047 Karlsen, K. Hvistendahl; Brusdal, K.; Dahle, H. K.; Evje, S.; Lie, K.-A. 18 1998 The multiscale restriction smoothed basis method for fractured porous media (F-MSRSB). Zbl 1349.76385 Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi 18 2016 Modelling of multiscale structures in flow simulations for petroleum reservoirs. Zbl 1178.76331 Aarnes, Jørg E.; Kippe, Vegard; Lie, Knut-Andreas; Rustad, Alf Birger 16 2007 On the importance of the Stokes-Brinkman equations for computing effective permeability in karst reservoirs. Zbl 1373.86003 Krotkiewski, Marcin; Ligaarden, Ingeborg S.; Lie, Knut-Andreas; Schmid, Daniel W. 16 2011 Unconditionally stable splitting methods for the shallow water equations. Zbl 0945.76059 Holdahl, Runar; Holden, Helge; Lie, Knut-Andreas 15 1999 Operator splitting methods for degenerate convection-diffusion equations. II: Numerical examples with emphasis on reservoir simulation and sedimentation. Zbl 1049.35113 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 13 2000 An unconditionally stable method for the Euler equations. Zbl 0922.76251 Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik 12 1999 Solving the Euler equations on graphics processing units. Zbl 1157.76358 Hagen, Trond Runar; Lie, Knut-Andreas; Natvig, Jostein R. 11 2006 Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Zbl 1392.86020 Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd 11 2016 A fast marching method for reservoir simulation. Zbl 0997.76062 Karlsen, K. Hvistendahl; Lie, K.-A.; Risebro, N. H. 10 2000 Fully implicit simulation of polymer flooding with MRST. Zbl 1401.76130 Bao, Kai; Lie, Knut-Andreas; Møyner, Olav; Liu, Ming 10 2017 Operator splitting methods for degenerate convection-diffusion equations. I: Convergence and entropy estimates. Zbl 0974.35065 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 8 2000 A multiscale two-point flux-approximation method. Zbl 1349.76368 Møyner, Olav; Lie, Knut-Andreas 8 2014 An improved quadrature rule for the flux computation in staggered central difference schemes in multidimensions. Zbl 1024.76030 Lie, Knut-Andreas; Noelle, Sebastian 8 2003 A simulation workflow for large-scale CO\(_2\) storage in the Norwegian North Sea. Zbl 1392.86015 Lie, Knut-Andreas; Nilsen, Halvor Møll; Andersen, Odd; Møyner, Olav 8 2016 How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine. Zbl 1126.65074 Hagen, Trond Runar; Henriksen, Martin O.; Hjelmervik, Jon M.; Lie, Knut-Andreas 7 2007 Dimensional splitting with front tracking and adaptive grid refinement. Zbl 0923.65061 Lie, K.-A.; Haugse, V.; Karlsen, K. Hvistendahl 7 1998 The localized reduced basis multiscale method for two-phase flows in porous media. Zbl 1352.76057 Kaulmann, S.; Flemisch, B.; Haasdonk, B.; Lie, K.-a.; Ohlberger, M. 7 2015 Fully implicit higher-order schemes applied to polymer flooding. Zbl 1396.76062 Mykkeltvedt, Trine S.; Raynaud, Xavier; Lie, Knut-Andreas 7 2017 Unstructured Voronoi grids conforming to lower dimensional objects. Zbl 1411.65155 Berge, Runar Lie; Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas 7 2019 Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. Zbl 0961.65073 Evje, S.; Karlsen, K. Hvistendahl; Lie, K. A.; Risebro, N. H. 6 2000 Simulation and visualization of the Saint-Venant system using GPUs. Zbl 1273.76338 Brodtkorb, André R.; Hagen, Trond R.; Lie, Knut-Andreas; Natvig, Jostein R. 6 2010 A front tracking method for conservation laws with boundary conditions. Zbl 0928.35098 Hvistendahl, K.; Lie, K.-A.; Risebro, N. H. 5 1999 Grid adaptation for the Dirichlet-Neumann representation method and the multiscale mixed finite-element method. Zbl 1386.76101 Lie, Knut-Andreas; Natvig, Jostein R.; Krogstad, Stein; Yang, Yahan; Wu, Xiao-Hui 5 2014 Scale space and variational methods in computer vision. Second international conference, SSVM 2009, Voss, Norway, June 1–5, 2009. Proceedings. Zbl 1233.68026 4 2009 Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations. Zbl 1330.76088 Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas 4 2015 The open porous media flow reservoir simulator. Zbl 1457.76107 Rasmussen, Atgeirr Flø; Sandve, Tor Harald; Bao, Kai; Lauser, Andreas; Hove, Joakim; Skaflestad, Bård; Klöfkorn, Robert; Blatt, Markus; Rustad, Alf Birger; Sævareid, Ove; Lie, Knut-Andreas; Thune, Andreas 4 2021 Discussion of dynamics and operator splitting techniques for two-phase flow with gravity. Zbl 1277.76119 Lie, Knut-Andreas; Natvig, Jostein R.; Nilsen, Halvor Møll 4 2012 Robust simulation of sharp-interface models for fast estimation of CO\(_2\) trapping capacity in large-scale aquifer systems. Zbl 1392.86021 Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd 4 2016 Efficient reordered nonlinear Gauss-Seidel solvers with higher order for black-oil models. Zbl 1434.86015 Klemetsdal, Øystein S.; Rasmussen, Atgeirr F.; Møyner, Olav; Lie, Knut-Andreas 4 2020 Multiscale methods for subsurface flow. Zbl 1364.76151 Aarnes, Jørg E.; Lie, Knut-Andreas; Kippe, Vegard; Krogstad, Stein 3 2009 Multiscale methods and streamline simulation for rapid reservoir performance prediction. Zbl 1309.76191 Aarnes, J. E.; Kippe, V.; Lie, K.-A. 3 2006 Efficient flow diagnostics proxies for polymer flooding. Zbl 1401.76137 Krogstad, Stein; Lie, Knut-Andreas; Nilsen, Halvor Møll; Berg, Carl Fredrik; Kippe, Vegard 3 2017 A fully implicit WENO scheme on stratigraphic and unstructured polyhedral grids. Zbl 1434.65150 Lie, Knut-Andreas; Mykkeltvedt, Trine S.; Møyner, Olav 2 2020 Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF. Zbl 1113.65002 1 2007 A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients. Zbl 0940.65109 Lie, Knut-Andreas 1 1999 Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients. Zbl 0954.35106 Lie, Knut-Andreas 1 2000 Operator splitting for convection-dominated nonlinear partial differential equations. Zbl 0989.65093 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik 1 2001 Image processing based on partial differential equations. Proceedings of the international conference on PDE-based image processing and related inverse problems, CMA, Oslo, Norway, August 8–12, 2005. Zbl 1107.68518 1 2007 On the resolution and stability of central difference schemes. Zbl 1063.65092 Lie, Knut-Andreas; Noelle, Sebastian; Rosenbaum, Wolfram 1 2002 Streamline simulation of a reactive advective flow with discontinuous flux function. Zbl 1414.76056 Ghaderi Zefreh, Masoud; Nilsen, Halvor M.; Lie, Knut Andreas; Raynaud, Xavier; Doster, Florian 1 2019 A comparison of consistent discretizations for elliptic problems on polyhedral grids. Zbl 1454.65147 Klemetsdal, Øystein S.; Møyner, Olav; Raynaud, Xavier; Lie, Knut-Andreas 1 2020 A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Zbl 1496.76133 Klemetsdal, Øystein; Moncorgé, Arthur; Møyner, Olav; Lie, Knut-Andreas 1 2022 Advanced Modelling with the MATLAB Reservoir Simulation Toolbox. Zbl 1473.86001 Lie, Knut-Andreas; Møyner, Olav 1 2021 A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Zbl 1496.76133 Klemetsdal, Øystein; Moncorgé, Arthur; Møyner, Olav; Lie, Knut-Andreas 1 2022 The open porous media flow reservoir simulator. Zbl 1457.76107 Rasmussen, Atgeirr Flø; Sandve, Tor Harald; Bao, Kai; Lauser, Andreas; Hove, Joakim; Skaflestad, Bård; Klöfkorn, Robert; Blatt, Markus; Rustad, Alf Birger; Sævareid, Ove; Lie, Knut-Andreas; Thune, Andreas 4 2021 Advanced Modelling with the MATLAB Reservoir Simulation Toolbox. Zbl 1473.86001 Lie, Knut-Andreas; Møyner, Olav 1 2021 Efficient reordered nonlinear Gauss-Seidel solvers with higher order for black-oil models. Zbl 1434.86015 Klemetsdal, Øystein S.; Rasmussen, Atgeirr F.; Møyner, Olav; Lie, Knut-Andreas 4 2020 A fully implicit WENO scheme on stratigraphic and unstructured polyhedral grids. Zbl 1434.65150 Lie, Knut-Andreas; Mykkeltvedt, Trine S.; Møyner, Olav 2 2020 A comparison of consistent discretizations for elliptic problems on polyhedral grids. Zbl 1454.65147 Klemetsdal, Øystein S.; Møyner, Olav; Raynaud, Xavier; Lie, Knut-Andreas 1 2020 An introduction to reservoir simulation using MATLAB/GNU Octave. User guide for the MATLAB reservoir simulation toolbox (MRST). Zbl 1425.76001 Lie, Knut-Andreas 69 2019 Unstructured Voronoi grids conforming to lower dimensional objects. Zbl 1411.65155 Berge, Runar Lie; Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas 7 2019 Streamline simulation of a reactive advective flow with discontinuous flux function. Zbl 1414.76056 Ghaderi Zefreh, Masoud; Nilsen, Halvor M.; Lie, Knut Andreas; Raynaud, Xavier; Doster, Florian 1 2019 Fully implicit simulation of polymer flooding with MRST. Zbl 1401.76130 Bao, Kai; Lie, Knut-Andreas; Møyner, Olav; Liu, Ming 10 2017 Fully implicit higher-order schemes applied to polymer flooding. Zbl 1396.76062 Mykkeltvedt, Trine S.; Raynaud, Xavier; Lie, Knut-Andreas 7 2017 Efficient flow diagnostics proxies for polymer flooding. Zbl 1401.76137 Krogstad, Stein; Lie, Knut-Andreas; Nilsen, Halvor Møll; Berg, Carl Fredrik; Kippe, Vegard 3 2017 A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. Zbl 1349.76824 Møyner, Olav; Lie, Knut-Andreas 44 2016 The multiscale restriction smoothed basis method for fractured porous media (F-MSRSB). Zbl 1349.76385 Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi 18 2016 Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Zbl 1392.86020 Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd 11 2016 A simulation workflow for large-scale CO\(_2\) storage in the Norwegian North Sea. Zbl 1392.86015 Lie, Knut-Andreas; Nilsen, Halvor Møll; Andersen, Odd; Møyner, Olav 8 2016 Robust simulation of sharp-interface models for fast estimation of CO\(_2\) trapping capacity in large-scale aquifer systems. Zbl 1392.86021 Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd 4 2016 The localized reduced basis multiscale method for two-phase flows in porous media. Zbl 1352.76057 Kaulmann, S.; Flemisch, B.; Haasdonk, B.; Lie, K.-a.; Ohlberger, M. 7 2015 Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations. Zbl 1330.76088 Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas 4 2015 A multiscale two-point flux-approximation method. Zbl 1349.76368 Møyner, Olav; Lie, Knut-Andreas 8 2014 Grid adaptation for the Dirichlet-Neumann representation method and the multiscale mixed finite-element method. Zbl 1386.76101 Lie, Knut-Andreas; Natvig, Jostein R.; Krogstad, Stein; Yang, Yahan; Wu, Xiao-Hui 5 2014 Open-source MATLAB implementation of consistent discretisations on complex grids. Zbl 1348.86002 Lie, Knut-Andreas; Krogstad, Stein; Ligaarden, Ingeborg Skjelkvåle; Natvig, Jostein Roald; Nilsen, Halvor Møll; Skaflestad, Bård 78 2012 Discussion of dynamics and operator splitting techniques for two-phase flow with gravity. Zbl 1277.76119 Lie, Knut-Andreas; Natvig, Jostein R.; Nilsen, Halvor Møll 4 2012 On the importance of the Stokes-Brinkman equations for computing effective permeability in karst reservoirs. Zbl 1373.86003 Krotkiewski, Marcin; Ligaarden, Ingeborg S.; Lie, Knut-Andreas; Schmid, Daniel W. 16 2011 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005 Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 75 2010 Simulation and visualization of the Saint-Venant system using GPUs. Zbl 1273.76338 Brodtkorb, André R.; Hagen, Trond R.; Lie, Knut-Andreas; Natvig, Jostein R. 6 2010 Scale space and variational methods in computer vision. Second international conference, SSVM 2009, Voss, Norway, June 1–5, 2009. Proceedings. Zbl 1233.68026 4 2009 Multiscale methods for subsurface flow. Zbl 1364.76151 Aarnes, Jørg E.; Lie, Knut-Andreas; Kippe, Vegard; Krogstad, Stein 3 2009 A comparison of multiscale methods for elliptic problems in porous media flow. Zbl 1259.76047 Kippe, Vegard; Aarnes, Jørg E.; Lie, Knut-Andreas 50 2008 Multiscale mixed/mimetic methods on corner-point grids. Zbl 1259.76065 Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas 38 2008 Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. Zbl 1218.76029 Natvig, Jostein R.; Lie, Knut-Andreas 23 2008 An introduction to the numerics of flow in porous media using Matlab. Zbl 1330.76004 Aarnes, Jørg E.; Gimse, Tore; Lie, Knut-Andreas 24 2007 Modelling of multiscale structures in flow simulations for petroleum reservoirs. Zbl 1178.76331 Aarnes, Jørg E.; Kippe, Vegard; Lie, Knut-Andreas; Rustad, Alf Birger 16 2007 How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine. Zbl 1126.65074 Hagen, Trond Runar; Henriksen, Martin O.; Hjelmervik, Jon M.; Lie, Knut-Andreas 7 2007 Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF. Zbl 1113.65002 1 2007 Image processing based on partial differential equations. Proceedings of the international conference on PDE-based image processing and related inverse problems, CMA, Oslo, Norway, August 8–12, 2005. Zbl 1107.68518 1 2007 A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Zbl 1124.76022 Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas 55 2006 Solving the Euler equations on graphics processing units. Zbl 1157.76358 Hagen, Trond Runar; Lie, Knut-Andreas; Natvig, Jostein R. 11 2006 Multiscale methods and streamline simulation for rapid reservoir performance prediction. Zbl 1309.76191 Aarnes, J. E.; Kippe, V.; Lie, K.-A. 3 2006 On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. Zbl 1038.65078 Lie, Knut-Andreas; Noelle, Sebastian 67 2003 An improved quadrature rule for the flux computation in staggered central difference schemes in multidimensions. Zbl 1024.76030 Lie, Knut-Andreas; Noelle, Sebastian 8 2003 On the resolution and stability of central difference schemes. Zbl 1063.65092 Lie, Knut-Andreas; Noelle, Sebastian; Rosenbaum, Wolfram 1 2002 Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. Zbl 1051.76046 Karlsen, K. Hvistendahl; Lie, K.-A.; Natvig, J. R.; Nordhaug, H. F.; Dahle, H. K. 24 2001 Operator splitting for convection-dominated nonlinear partial differential equations. Zbl 0989.65093 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik 1 2001 Operator splitting methods for degenerate convection-diffusion equations. II: Numerical examples with emphasis on reservoir simulation and sedimentation. Zbl 1049.35113 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 13 2000 A fast marching method for reservoir simulation. Zbl 0997.76062 Karlsen, K. Hvistendahl; Lie, K.-A.; Risebro, N. H. 10 2000 Operator splitting methods for degenerate convection-diffusion equations. I: Convergence and entropy estimates. Zbl 0974.35065 Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 8 2000 Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. Zbl 0961.65073 Evje, S.; Karlsen, K. Hvistendahl; Lie, K. A.; Risebro, N. H. 6 2000 Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients. Zbl 0954.35106 Lie, Knut-Andreas 1 2000 An unconditionally stable splitting scheme for a class of nonlinear parabolic equations. Zbl 0949.65089 Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 22 1999 Unconditionally stable splitting methods for the shallow water equations. Zbl 0945.76059 Holdahl, Runar; Holden, Helge; Lie, Knut-Andreas 15 1999 An unconditionally stable method for the Euler equations. Zbl 0922.76251 Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik 12 1999 A front tracking method for conservation laws with boundary conditions. Zbl 0928.35098 Hvistendahl, K.; Lie, K.-A.; Risebro, N. H. 5 1999 A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients. Zbl 0940.65109 Lie, Knut-Andreas 1 1999 The corrected operator splitting approach applied to a nonlinear advection-diffusion problem. Zbl 0942.76047 Karlsen, K. Hvistendahl; Brusdal, K.; Dahle, H. K.; Evje, S.; Lie, K.-A. 18 1998 Dimensional splitting with front tracking and adaptive grid refinement. Zbl 0923.65061 Lie, K.-A.; Haugse, V.; Karlsen, K. Hvistendahl 7 1998 all cited Publications top 5 cited Publications all top 5 Cited by 1,137 Authors 42 Kurganov, Alexander 33 Lie, Knut-Andreas 23 Hajibeygi, Hadi 22 Tchelepi, Hamdi A. 19 Karlsen, Kenneth Hvistendahl 18 Chertock, Alina E. 18 Møyner, Olav 18 Nilsen, Halvor Møll 18 Risebro, Nils Henrik 14 Yang, Haijian 13 Sun, Shuyu 11 Liu, Yongle 11 Zabaras, Nicholas J. 10 Hamon, François P. 10 Jenny, Patrick 10 Krogstad, Stein 10 Yang, Chao 9 Efendiev, Yalchin R. 8 Castelletto, Nicola 8 Dong, Jian 8 Holden, Helge 8 Manzini, Gianmarco 8 Nordbotten, Jan Martin 7 Andersen, Odd A. 7 Chung, Tsz Shun Eric 7 Jansen, Jan-Dirk 7 Raynaud, Xavier 6 Abreu, Eduardo 6 Galvis, Juan 6 Geiser, Jürgen 6 Kacur, Jozef 6 Keilegavlen, Eirik 6 Lipnikov, Konstantin N. 6 Liu, Xin 6 Moncorgé, Arthur 6 Natvig, Jostein Roald 6 Ohlberger, Mario 5 Berre, Inga 5 Bürger, Raimund 5 Foss, Bjarne A. 5 Gildin, Eduardo 5 King, Michael J. 5 Klemetsdal, Øystein Strengehagen 5 Lukáčová-Medviďová, Mária 5 Noelle, Sebastian 5 Schratz, Katharina 5 Ţene, Matei 5 Tomin, Pavel 5 Yotov, Ivan 4 Brezzi, Franco 4 Brodtkorb, André Rigland 4 Chu, Shaoshuai 4 Csomós, Petra 4 Cusini, Matteo 4 Florez, Horacio 4 Fumagalli, Alessio 4 Helmig, Rainer 4 Kumar, Kundan 4 Leung, Wingtat 4 Li, Dingfang 4 Li, Yiteng 4 Mehmani, Yashar 4 Mishra, Siddhartha 4 Presho, Michael 4 Remešiková, Mariana 4 Ruiz-Baier, Ricardo 4 Sandve, Tor Harald 4 Sousa, Fabrício S. 4 Vassilevski, Panayot Spirov 4 Wheeler, Mary Fanett 4 White, Joshua A. 4 Zeitlin, Vladimir 4 Zhang, Na 3 Aarnes, Jørg E. 3 Arshad, Muhammad 3 Ausas, Roberto Federico 3 Bao, Kai 3 Bátkai, András 3 Bosma, Sebastian B. M. 3 Buscaglia, Gustavo Carlos 3 Cai, Xiao-Chuan 3 Cao, Yangyang 3 Capolei, Andrea 3 Chen, Huangxin 3 Cheng, Tianpei 3 de Moraes, Rafael J. 3 Edwards, Michael G. 3 Elsheikh, Ahmed H. 3 Farkas, Bálint 3 Flemisch, Bernd 3 Formaggia, Luca 3 Grana, Dario 3 Guerrero, Francisco 3 Herty, Michael Matthias 3 Huang, ZhaoQin 3 Jackson, Matthew D. 3 Jerez, Silvia 3 Jiang, Jiamin 3 Jørgensen, John Bagterp 3 Keyes, David Elliot ...and 1,037 more Authors all top 5 Cited in 108 Serials 132 Journal of Computational Physics 121 Computational Geosciences 34 Computer Methods in Applied Mechanics and Engineering 23 Journal of Scientific Computing 21 Computers & Mathematics with Applications 21 Journal of Computational and Applied Mathematics 14 SIAM Journal on Scientific Computing 13 Computers and Fluids 11 Applied Mathematics and Computation 11 Applied Numerical Mathematics 10 Communications in Computational Physics 9 Mathematics of Computation 9 Numerische Mathematik 9 Multiscale Modeling & Simulation 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Numerical Methods for Partial Differential Equations 6 Computer Physics Communications 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Advances in Computational Mathematics 5 International Journal for Numerical Methods in Fluids 5 Journal of Fluid Mechanics 5 Applied Mathematical Modelling 4 Journal of Mathematical Analysis and Applications 4 BIT 4 International Journal for Numerical Methods in Engineering 4 SIAM Journal on Numerical Analysis 4 Mathematical Geosciences 4 Journal of Computational Physics: X 3 Computing and Visualization in Science 3 International Journal of Computational Fluid Dynamics 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Optimization and Engineering 2 Acta Mechanica 2 Journal of Engineering Mathematics 2 Journal of Differential Equations 2 Computational Mechanics 2 Applications of Mathematics 2 Computational Mathematics and Mathematical Physics 2 International Journal of Computer Mathematics 2 SIAM Journal on Mathematical Analysis 2 Computational and Applied Mathematics 2 Engineering Analysis with Boundary Elements 2 Discrete and Continuous Dynamical Systems 2 Discrete and Continuous Dynamical Systems. Series B 2 International Journal of Computational Methods 2 Journal of Hyperbolic Differential Equations 2 Acta Numerica 2 International Journal of Numerical Analysis and Modeling 2 Networks and Heterogeneous Media 2 Journal of Mathematics in Industry 2 SMAI Journal of Computational Mathematics 1 Geophysical and Astrophysical Fluid Dynamics 1 Inverse Problems 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Bulletin of Mathematical Biology 1 Applied Mathematics and Optimization 1 Calcolo 1 Integral Equations and Operator Theory 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Mathematics and Computers in Simulation 1 Meccanica 1 Semigroup Forum 1 Physica D 1 Parallel Computing 1 Mathematical and Computer Modelling 1 Journal of Integral Equations and Applications 1 Numerical Algorithms 1 Computational Optimization and Applications 1 Numerical Linear Algebra with Applications 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Turkish Journal of Mathematics 1 Filomat 1 Journal of Mathematical Chemistry 1 Mathematical Problems in Engineering 1 Doklady Mathematics 1 Vietnam Journal of Mathematics 1 Mathematical and Computer Modelling of Dynamical Systems 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 Communications in Nonlinear Science and Numerical Simulation 1 Lobachevskii Journal of Mathematics 1 Foundations of Computational Mathematics 1 Journal of Numerical Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 SIAM Journal on Applied Dynamical Systems 1 Advances in Difference Equations 1 Parallel Processing Letters 1 Mathematical Biosciences and Engineering 1 Journal of Industrial and Management Optimization 1 Acta Mechanica Sinica 1 Kinetic and Related Models 1 Advances in Applied Mathematics and Mechanics 1 GEM - International Journal on Geomathematics 1 Numerical Algebra, Control and Optimization 1 Iranian Journal of Mathematical Sciences and Informatics 1 ISRN Applied Mathematics 1 Journal of Applied Analysis and Computation 1 Forum of Mathematics, Pi ...and 8 more Serials all top 5 Cited in 32 Fields 422 Numerical analysis (65-XX) 387 Fluid mechanics (76-XX) 206 Partial differential equations (35-XX) 119 Geophysics (86-XX) 48 Mechanics of deformable solids (74-XX) 23 Biology and other natural sciences (92-XX) 19 Operations research, mathematical programming (90-XX) 18 Computer science (68-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 13 Probability theory and stochastic processes (60-XX) 12 Statistics (62-XX) 8 Ordinary differential equations (34-XX) 8 Operator theory (47-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Optics, electromagnetic theory (78-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Approximations and expansions (41-XX) 2 Combinatorics (05-XX) 2 Special functions (33-XX) 2 Integral equations (45-XX) 2 Quantum theory (81-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year