二维半线性波动方程的能量稳定的Galerkin方法超收敛分析

Superconvergence Analysis of an Energy-Stable Galerkin Method for Two-Dimensional Semilinear Wave Equation

文章研究了一类半线性波动方程的能量稳定的全离散Galerkin方法的超收敛误差估计。首先,分析了数值格式解的唯一性和稳定性。其次,利用矩形网格上双线性元的特殊性质以及插值算子和Ritz算子在H1-范数下的超逼近的估计,得到了超逼近的结果。再次,借助于插值后处理技术得到了H1-范数下的全局超收敛的结果。最后,通过数值实验验证了理论分析的正确性。

In this paper,an implicit fully-discrete energy-stable Galerkin scheme is proposed and investigated for the semilinear wave equation.Firstly,the unique solvability and the stability of the numerical solution are studied.Then,in terms of the special property of the bilinear element on the rectangular mesh and the supercolose estimate between interpolation operator and Ritz operator in H1-norm,the global superconvergence result in H1-norm is ob⁃tained using a post-processing technique.Finally,numerical experiment is performed to support the theoretical find⁃ings.