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

In this paper, we present a high-order weak Galerkin finite element method (WG-FEM) for solving the H(curl;Omega$$ \Omega $$)-elliptic problems with interfaces in & Ropf;d(d=2,3)$$ {\mathbb{R}}<^>d\left(d=2,3\right) $$. 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 k >= 1$$ k\ge 1 $$. Necessary stabilizations are enforced to ensure weak tangential continuity of approximation functions. Optimal convergence rates of order k+1$$ k+1 $$ under L2$$ {L}<^>2 $$-norm and order k$$ k $$ in a discrete H(curl)$$ \mathbf{H}\left(\operatorname{curl}\right) $$-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.