Virtual elements for Maxwell's equations

2021/02/01 by da Veiga, L. Beirão, Dassi, F., Manzini, G. +1 · 1 citation
#65N12 #65N15 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2102.00950

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.

Cited by

• A higher order pressure-stabilized virtual element formulation for the Stokes-Poisson-Boltzmann equations

Related

• Interpolation and stability properties of low order face and edge virtual element spaces
• The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
• A Yee-like finite-element scheme for Maxwell's equations on unstructured grids
• Energy Conserving Higher Order Mixed Finite Element Discretizations of Maxwell's Equations
• Finite Element Methods for Maxwell's Equations