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
Recommended Citation
AZAIEZ, A, BENJEMAA, M, JRAJRIA, A, & ZAAG, H (2023). Discontinuous Galerkin method for blow-up solutions of nonlinear wave equations. Turkish Journal of Mathematics 47 (3): 1015-1038. https://doi.org/10.55730/1300-0098.3408
