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Turkish Journal of Mathematics

Abstract

e develop and study an explicit time-space discrete discontinuous Galerkin finite element 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 examples and benchmarks.

DOI

10.55730/1300-0098.3408

Keywords

Nonlinear wave equation, discontinuous Galerkin methods, numerical blow-up, numerical analysis

First Page

1015

Last Page

1038

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