This presentation will be given online by zoom, with the zoom link sent to the AMC seminar list. Participants interested in viewing should sign up for that list (see AMC Seminar website).
The virtual element method (VEM) is a generalization of the classic finite element method (FEM). In the VEM framework the shape functions used to approximate the solution to PDE systems can be proven to exist but no explicit formula can be attained, thus they are said to be virtual. The "name of the game" in this method is to define a series of projectors onto polynomial spaces where an explicit basis is known and can be used to come up with approximations to mass and stiffness matrices. In this presentation we will discuss the design of a VEM for the kinematics of magnetohydrodynamics (MHD) which is a coupling between electromagnetics and fluid flow describing the behaviour of magnetized fluids. Implementations of VEM for MHD present two major advantages, the first is the possibility of its implementation in a very general class of meshes making VEM well-suited for problems posed in oddly shaped domains or with irregularly shaped material interfaces. The second involves the divergence of the magnetic field, it should remain close to zero at the discrete level in order to prevent the appearance of fictitious forces that render simulations unfaithful to the true physics involved, VEM captures this feature exactly as we will prove theoretically and verify numerically.