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Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes

Congreve, Scott; Houston, Paul

Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes Thumbnail


Authors

Scott Congreve

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths



Abstract

This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated polygonal/polyhedral meshes are employed for the coarse mesh approximation. We recall that within the two-grid setting, while it is necessary to solve a nonlinear problem on the coarse approximation space, only a linear problem must be computed on the original fine finite element space. In this article, the coarse space will be constructed by agglomerating elements from the original fine mesh. Here, we extend the existing a priori and a posteriori error analysis for the two-grid hp-version discontinuous Galerkin finite element method from Congreve et al. [1]for coarse meshes consisting of standard element shapes to include arbitrarily agglomerated coarse grids. Moreover, we develop an hp-adaptive two-grid algorithm to adaptively design the fine and coarse finite element spaces; we stress that this is undertaken in a fully automatic manner, and hence can be viewed as blackbox solver. Numerical experiments are presented for two- and three-dimensional problems to demonstrate the computational performance of the proposed hp-adaptive two-grid method.

Citation

Congreve, S., & Houston, P. (2022). Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes. Advances in Computational Mathematics, 48(5), Article 54. https://doi.org/10.1007/s10444-022-09968-w

Journal Article Type Article
Acceptance Date Jun 20, 2022
Online Publication Date Aug 11, 2022
Publication Date Aug 11, 2022
Deposit Date Jun 27, 2022
Publicly Available Date Mar 29, 2024
Journal Advances in Computational Mathematics
Print ISSN 1019-7168
Electronic ISSN 1572-9044
Publisher Springer Science and Business Media LLC
Peer Reviewed Peer Reviewed
Volume 48
Issue 5
Article Number 54
DOI https://doi.org/10.1007/s10444-022-09968-w
Keywords Applied Mathematics; Computational Mathematics
Public URL https://nottingham-repository.worktribe.com/output/8762755
Publisher URL https://link.springer.com/article/10.1007/s10444-022-09968-w
Additional Information The version of record of this article, first published in Advances in Computational Mathmatics, is available online at Publisher’s website: http://dx.doi.org/10.1007/s10444-022-09968-w

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