Virtual elements for Maxwell's equations
L. Beirão da Veiga, Franco Dassi, Gianmarco Manzini, Lorenzo Mascotto
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 associated with de Rahm sequences of nodal, edge, and face virtual element spaces.
Topics & Concepts
DiscretizationMathematicsPolygon meshMaxwell's equationsA priori and a posterioriElement (criminal law)Set (abstract data type)Applied mathematicsFinite element methodFace (sociological concept)Mathematical analysisCalculus (dental)GeometryComputer scienceDentistryPhilosophyPhysicsPolitical scienceThermodynamicsSociologyLawEpistemologySocial scienceMedicineProgramming languageAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsAdvanced Mathematical Modeling in Engineering