A Priori Error Estimates for H(curl)$$ \mathbf{H}\left(\operatorname{curl}\right) $$ and H(div)$$ \mathbf{H}\left(\operatorname{div}\right) $$‐Elliptic Interface Problems: Least‐Squares Weak Galerkin Finite Element Methods

ABSTRACT In this article, least‐squares weak Galerkin finite element methods are presented to solve the and ‐elliptic interface problems with non‐homogeneous jump conditions in both primal and flux variables. The proposed methods enable the incorporation of discontinuous functions within mesh element partitions composed of general polytopal elements. Optimal‐order error estimates have been derived for both flux and primal unknowns. A series of numerical tests for the proposed problems has been conducted to corroborate our theoretical findings, encompassing interfaces of varying smoothness and complexity.