An explicit discontinuous Galerkin method for blow-up solutions of nonlinear wave equations
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In this work, we develop and study a discontinuous Galerkin (DG) method to approximate the solution of 1D nonlinear wave equations. We show that the numerical scheme is consistent, stable and convergent if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that the numerical blow-up time converges toward the theoretical one. The validity of our results is confirmed throughout several numerical examples and benchmarks.
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