| Issue |
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
|
|
|---|---|---|
| Page(s) | 2255 - 2296 | |
| DOI | https://doi.org/10.1051/m2an/2022066 | |
| Published online | 08 December 2022 | |
Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations
Department of Mathematics, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
* Corresponding author: aili.shao@maths.ox.ac.uk
Received:
17
December
2021
Accepted:
5
September
2022
In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a hp-version discontinuous Galerkin finite element approximation in the time direction with an H1(Ω)-conforming finite element approximation in the spatial variables. Error bounds at the temporal nodal points are derived under a weak restriction on the temporal step size in terms of the spatial mesh size. Numerical experiments are presented to verify the theoretical results.
Mathematics Subject Classification: 65M60 / 65M12 / 35L72 / 35L53
Key words: Numerical analysis / finite element method / discontinuous Galerkin method / second-order nonlinear hyperbolic PDEs / nonlinear systems of PDEs / nonlinear elastodynamics equations
© The authors. Published by EDP Sciences, SMAI 2022
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