Broken-FEEC on multipatch domains with local refinements

Abstract: This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous discretizations at patch interfaces, preserving the de Rham structure and offering computational benefits. However, local refinements often lead to numerical artifacts. Our solution involves developing moment-preserving discrete conforming projection operators. These operators are explicit, localized, and metric-independent, ensuring $H^1$ and $H(\text{curl})$ continuity across non-matching interfaces while preserving high-order polynomial moments. This results in broken-FEEC de Rham sequences with accurate strong and weak derivatives, leading to energy-preserving Maxwell solvers that are explicit and virtually free of spurious modes. Numerical simulations confirm the efficacy of our method in eliminating spurious waves.