The nonconforming virtual element method for semilinear elliptic problems

作者：

Highlights：

• In this paper, we develop the nonconforming VEM to semilinear elliptic equation on polygonal or polyhedral meshes. One advantage of nonconforming VEM is that it can deal with two and three dimensional problems at the same time, which brings convenience to analysis. The nonlinear right-hand side is approximated by using the L2 projection. The optimal error estimation for the nonconforming VEM in the broken H1 semi-norm is obtained. Numerical experiments are given to verify the correctness of the theoretical analysis.

摘要

•In this paper, we develop the nonconforming VEM to semilinear elliptic equation on polygonal or polyhedral meshes. One advantage of nonconforming VEM is that it can deal with two and three dimensional problems at the same time, which brings convenience to analysis. The nonlinear right-hand side is approximated by using the L2 projection. The optimal error estimation for the nonconforming VEM in the broken H1 semi-norm is obtained. Numerical experiments are given to verify the correctness of the theoretical analysis.

论文关键词：Nonconforming virtual element,Semilinear elliptic problem,Polygonal or polyhedral mesh

论文评审过程：Received 15 January 2022, Revised 3 July 2022, Accepted 10 July 2022, Available online 17 July 2022, Version of Record 17 July 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127402