An Lp- primal-dual weak Galerkin method for div-curl systems

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 W alpha ,p-regularity (alpha > 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 p1 + 1q = 1. A series of numerical experiments are presented to demonstrate the performance of the proposed Lp-PDWG algorithm. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a new Lp-primal-dual weak Galerkin finite element method for solving the div-curl system with the normal boundary condition. The proposed method provides accurate and reliable numerical solutions under low Wα,p-regularity and offers effective approximations of normal harmonic vector fields on domains with complex topology.