A Discontinuous Galerkin Method for the Fourth-Order Curl Problem

Abstract

In this paper, we present a discontinuous Galerkin (DG) method based on the Nédélec finite element space for solving a fourth-order curl equation arising from a magnetohydrodynamics model on a 3-dimensional bounded Lipschitz polyhedron. We show that the method has an optimal error estimate for a model problem involving a fourth-order curl operator. Furthermore, some numerical results in 2 dimensions are presented to verify the theoretical results.