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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.

Details

Date:
April 27, 2018
Time:
4:10 pm - 5:15 pm
Event Category: