A parallel iterative procedure for weak Galerkin methods for second order elliptic problems

TL;DR

This paper introduces a parallel iterative method based on domain decomposition for weak Galerkin finite element solutions of second order elliptic problems, with proven convergence and verified through numerical tests.

Contribution

It develops a new parallelizable iterative procedure for weak Galerkin methods, including convergence analysis for domain decompositions into elements or larger subdomains.

Findings

Convergence of the iterative method is established theoretically.

Numerical tests confirm the effectiveness and accuracy of the proposed method.

The method is suitable for parallel computing environments.

Abstract

A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the domain into individual elements associated to the weak Galerkin methods or into larger subdomains. A series of numerical tests are illustrated to verify the theory developed in this paper.