The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients

Highlights：

• The space-time CG method presented in this paper is a kind of high accuracy numerical method and have the good stability. Moreover, it allows the change of the space-time grid structure, which make it very suitable for designing and analyzing adaptive algorithm on unstructured mesh.

• The study work presented in this article lays a solid foundation for solving the time-dependent nonlinear problems with linearized space-time CG method.

摘要

•It is the first time that this paper uses the space-time continuous Galerkin (CG) method to give the study for the problems with space-time variable coefficients. It further develops and perfects the existing space-time CG method.•The space-time CG method presented in this paper is a kind of high accuracy numerical method and have the good stability. Moreover, it allows the change of the space-time grid structure, which make it very suitable for designing and analyzing adaptive algorithm on unstructured mesh.•The study work presented in this article lays a solid foundation for solving the time-dependent nonlinear problems with linearized space-time CG method.

论文关键词：Continuous Galerkin method,Sobolev equation with space-time variable coefficients,A priori error estimation,Numerical experiments

论文评审过程：Received 31 July 2020, Revised 9 December 2020, Accepted 14 January 2021, Available online 21 February 2021, Version of Record 21 February 2021.