A Parallel iterative Algorithm for primal-dual weak Galerkin Schemes

Abstract: This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poisson equation. The existence and uniqueness of the PDWG solution are established. Optimal order of error estimates are derived in both a discrete norm and the $L^2$ norm. The convergence analysis is conducted for domain decompositions into individual elements associated with the PDWG methods, which can be extended to larger subdomains without any difficulty.