An Efficient and Robust Weak Galerkin Scheme for Solving the 2D/3D H(curl;Ω)‐Elliptic Interface Problems With High‐Order Elements

ABSTRACT In this paper, we present a high‐order weak Galerkin finite element method (WG‐FEM) for solving the H (curl;)‐elliptic problems with interfaces in . As applied to curl–curl problems, the weak Galerkin method uses two operators: weak curl and discrete weak curl projected in a polynomial space of degree . Necessary stabilizations are enforced to ensure weak tangential continuity of approximation functions. Optimal convergence rates of order under ‐norm and order in a discrete ‐like norm are established on hybrid meshes. Numerical experiments verify the expected order of accuracy for both two‐dimensional and three‐dimensional examples. At the same time, this method is able to accommodate geometrically complicated interfaces and has low regularity requirements.