High accuracy analysis of Galerkin finite element method for Klein–Gordon–Zakharov equations

作者：

Highlights：

• We propose a Galerkin finite element method (FEM) for solving the Klein–Gordon–Zakharov equations with power law nonlinearity.

• we use the combination of the interpolation and Ritz projection technique, which can reduce the regularity of exact solution.

• We study the optimal and superconvergent error estimate results both theoretically and numerically.

• We discuss the extensions of our scheme to more general finite elements.

摘要

•We propose a Galerkin finite element method (FEM) for solving the Klein–Gordon–Zakharov equations with power law nonlinearity.•we use the combination of the interpolation and Ritz projection technique, which can reduce the regularity of exact solution.•We study the optimal and superconvergent error estimate results both theoretically and numerically.•We discuss the extensions of our scheme to more general finite elements.

论文关键词：KGZ equations,Bilinear Galerkin FEM,Combination technique,Superclose and superconvergence,Optimal error estimation

论文评审过程：Received 8 April 2021, Revised 2 September 2021, Accepted 26 September 2021, Available online 18 October 2021, Version of Record 18 October 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126701