Authors: ASMA AZAIEZ, MONDHER BENJEMAA, AIDA JRAJRIA, HATEM ZAAG

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.

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

Full Text: PDF