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.
Nonlinear wave equation, discontinuous Galerkin methods, numerical blow-up, numerical analysis
AZAIEZ, ASMA; BENJEMAA, MONDHER; JRAJRIA, AIDA; and ZAAG, HATEM
"Discontinuous Galerkin method for blow-up solutions of nonlinear wave equations,"
Turkish Journal of Mathematics: Vol. 47:
3, Article 8.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss3/8