A family of three-dimensional virtual elements with applications to magnetostatic

Abstract

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H(\mathbf{curl})$-conforming ($1$-forms), and $H(\mathrm{div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.

Submitted to SINUM

References in corpus (3)

• A Stress/Displacement Virtual Element Method for Plane Elasticity Problems
• Lowest order Virtual Element approximation of magnetostatic problems
• Some Error Analysis on Virtual Element Methods

Cited by in corpus (1)

• Parallel solvers for virtual element discretizations of elliptic equations in mixed form