A Primal-Dual Weak Galerkin Method for Div-Curl Systems with low-regularity solutions

03/26/2020

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by   Yujie Liu, et al.

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This article presents a new primal-dual weak Galerkin finite element method for the tangential boundary value problem of div-curl systems with low-regularity solutions. The numerical scheme is based on a weak formulation, called the primal equation, involving no partial derivatives for the exact solution supplemented by the its dual form in the context of weak Galerkin. Optimal order error estimates in L^2 are established for vector fields with H^α(Ω)-regularity, α>0. The mathematical theory was derived for connected domains with general topological properties (namely, arbitrary Betti numbers). Numerical results are reported to not only verify the theoretical convergence but also demonstrate the performance of the new method.