论文标题
非线性1D波方程的爆炸解决方案的不连续galerkin方法
Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations
论文作者
论文摘要
我们开发和研究了一个时间空间离散的不连续的Galerkin有限元方法，以近似一维非线性波方程的解。我们表明，如果考虑不均匀的时间网格，数值方案是稳定的。我们还研究了爆炸现象，并证明在弱收敛假设下，数值爆炸时间趋向于理论上。在几个数值示例和基准中，我们的结果的有效性得到了证实。
We develop and study a time-space discrete discontinuous Galerkin finite elements 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 numerical examples and benchmarks.
