An [formula omitted]- primal–dual weak Galerkin method for div–curl systems

Abstract

This paper presents a new Lp-primal–dual weak Galerkin (PDWG) finite element method for the div–curl system with the normal boundary condition for p>1. Two crucial features for the proposed Lp-PDWG finite element scheme are as follows: (1) it offers an accurate and reliable numerical solution to the div–curl system under the low Wα,p-regularity (α>0) assumption for the exact solution; (2) it offers an effective approximation of the normal harmonic vector fields on domains with complex topology. An optimal order error estimate is established in the Lq-norm for the primal variable where 1p+1q=1. A series of numerical experiments are presented to demonstrate the performance of the proposed Lp-PDWG algorithm.