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Event Type:

M.Sc. Presentation

Date/Time:

Monday, May 13, 2019 - 12:00 to 13:00

Location:

Kidder room 274

Local Speaker:

Abstract:

We present a virtual element method (VEM) for the equations of magnetohydrodynamics (MHD). These equations describe the evolution of the electric and magnetic fields of a fluid that has a prescribed flow. This method is designed work in very general class of meshes and to preserve the divergence free condition on the magnetic field as dictated by Gauss's law. A sufficient condition for the stability of the method is presented. The construction of the mass matrices is done in the mimetic finite difference (MFD) framework, thus serving as a boundary object to compare and contrast the two frameworks. Finally, we present an experimental study of convergence for three types of meshes: with triangular cells, perturbed quadrilaterals and unstructured polyhedrons that we obtain from Voronoi tessellations.