An Extended Galerkin analysis in finite element exterior calculus

Abstract

For the Hodge-Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contractible domains, this framework utilizes seven fields and provides a unifying inf-sup analysis with respect to all discretization and penalty parameters. It is shown that the proposed methods can be hybridized as a reduced two-field formulation.

Nodal auxiliary space preconditioning for the surface de Rham complex

“…In finite element exterior calculus, the Hodge-Laplace equation is an important model problem under extensive investigation in recent years (cf. [4,6,36,23,39,37]). When solving the discrete Hodge Laplacian on domains with nontrivial topology, it is crucial to capture its kernel, the space of discrete harmonic forms or harmonic vector fields.…”