Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations
Analysis of PDEs
2021-04-07 v2 Numerical Analysis
Numerical Analysis
Abstract
We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several numerical examples and benchmarks.
Cite
@article{arxiv.2008.02659,
title = {Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations},
author = {Asma Azaiez and Mondher Benjemaa and Aida Jrajria and Hatem Zaag},
journal= {arXiv preprint arXiv:2008.02659},
year = {2021}
}
Comments
34 pages, 8 figures, 3 tables