An L^p- Primal-Dual Weak Galerkin method for div-curl Systems
share
This paper presents a new L^p-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 L^p-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^α, 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 L^q-norm for the primal variable where 1/p+1/q=1. A series of numerical experiments are presented to demonstrate the performance of the proposed L^p-PDWG algorithm.
READ FULL TEXT