Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs

In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first ap...

Full description

Bibliographic Details
Main Authors: Congreve, Scott, Houston, Paul, Wihler, Thomas P.
Format: Article
Published: Wiley-VCH 2011
Online Access:https://eprints.nottingham.ac.uk/1481/
_version_ 1848790614910435328
author Congreve, Scott
Houston, Paul
Wihler, Thomas P.
author_facet Congreve, Scott
Houston, Paul
Wihler, Thomas P.
author_sort Congreve, Scott
building Nottingham Research Data Repository
collection Online Access
description In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented.
first_indexed 2025-11-14T18:15:25Z
format Article
id nottingham-1481
institution University of Nottingham Malaysia Campus
institution_category Local University
last_indexed 2025-11-14T18:15:25Z
publishDate 2011
publisher Wiley-VCH
recordtype eprints
repository_type Digital Repository
spelling nottingham-14812020-05-04T20:23:47Z https://eprints.nottingham.ac.uk/1481/ Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs Congreve, Scott Houston, Paul Wihler, Thomas P. In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented. Wiley-VCH 2011 Article PeerReviewed Congreve, Scott, Houston, Paul and Wihler, Thomas P. (2011) Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proceedings in Applied Mathematics and Mechanics, 11 (1). pp. 3-6. ISSN 1617-7061 http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110002/pdf doi:10.1002/pamm.201110002 doi:10.1002/pamm.201110002
spellingShingle Congreve, Scott
Houston, Paul
Wihler, Thomas P.
Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title_full Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title_fullStr Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title_full_unstemmed Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title_short Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
title_sort two-grid hp-version dgfems for strongly monotone second-order quasilinear elliptic pdes
url https://eprints.nottingham.ac.uk/1481/
https://eprints.nottingham.ac.uk/1481/
https://eprints.nottingham.ac.uk/1481/