Virtual elements for Maxwell's equations

Abstract

We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori estimates and validate them on a set of numerical experiments. As pivot results, we discuss some novel inequalities for de Rahm sequences of nodal, edge, and face virtual element spaces.

References in corpus (3)

• A Recursive Algebraic Coloring Technique for Hardware-Efficient Symmetric Sparse Matrix-Vector Multiplication
• Lowest order Virtual Element approximation of magnetostatic problems
• Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

Cited by in corpus (2)

• Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
• A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh