非线性一维wave equations爆破解的间断Galerkin方法
Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations
摘要：
本文发展和研究了一维非线性波动方程的时空离散间断Galerkin有限元方法。我们表明，数值方案是稳定的，如果被认为是一个非均匀时间网格。我们还研究了爆破现象，证明了在弱收敛假设下，数值爆破时间趋向于理论爆破时间。通过几个数值例子和基准，我们的结果的有效性得到证实。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
