An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e3546" altimg="si714.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>- 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 normal boundary condition p>1. Two crucial features proposed Lp-PDWG scheme are as follows: (1) it offers an accurate and reliable numerical solution to under low W?,p-regularity (?>0) assumption exact solution; (2) effective approximation of harmonic vector fields on domains complex topology. An optimal order error estimate is established in Lq-norm primal variable where 1p+1q=1. A series experiments presented demonstrate performance algorithm.