International Journal of Nonlinear Analysis and Applications

The lowest-degree stabilizer-free weak Galerkin finite element method for Poisson equation on rectangular and triangular meshes

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar Iran

Abstract

Recently, the study on weak Galerkin (WG) methods with or without stabilizer parameters has received much attention. The WG methods are a discontinuous extension of the standard finite element methods in which classical differential operators are approximated on functions with discontinuity. A stabilizer term in the WG formulation is used to guarantee convergence and stability of the discontinuous approximations for a model problem. By removing this parameter, we can reduce the complexity of programming on this numerical method. Our goal in this paper is to introduce a new stabilizer-free WG (SFWG) method to solve the Poisson equation in which we use a new combination of WG elements. Numerical experiments indicate that our SFWG scheme is faster and more economical than the standard WG scheme. Errors and convergence rates on two types of mesh are presented for each of the considered methods, which show that our numerical scheme has $O(h^2)$ convergence rate while another method has $O(h)$ convergence rate in the energy norm and the $L^2$-norm.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 83-94
  • Receive Date: 01 September 2021
  • Revise Date: 27 October 2021
  • Accept Date: 31 October 2021