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Tobin Isaac, Georgia Tech – Applied Mathematics Colloquium
April 27, 2018 @ 4:10 pm - 5:15 pm
332 Phillips Hall, 4:10 pm – 5:15 pm
No tea this week
Title: Mixed Finite Element Extensions of MAC Schemes
Abstract: The Marker-and-Cell (MAC) discretization is a surprisingly efficient discretization for Stokes equations, converging at second order with a small number of degrees of freedom and sparse stencil. But that second order convergence can be explained by a cancellation of errors, which makes it fragile. Can we maintain second order convergence for MAC discretizations on deformed or non-conforming grids, or for creeping flows with anisotropic effective viscosities? We develop an approach for a version of this problem on tetrahedral meshes, combining weakly-symmetric discretizations from the study of linear elasticity with multipoint flux methods to eliminate auxiliary fields that get introduced along the way, leaving a scheme with the same variables as a MAC scheme and robust second order convergence. We will also discuss the work to be done to extend this approach to hexahedral MAC schemes.