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arXiv · 2008.02659

Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations

Asma Azaiez·Mondher Benjemaa·Aida Jrajria·Hatem Zaag
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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.

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Asma Azaiez, Mondher Benjemaa, Aida Jrajria, Hatem Zaag. 2020-08-06. Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations. https://arxiv.org/abs/2008.02659

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