Finite Element Transport using Wachspress Rational Functions on Quadrilaterals in Diffusive Regions

Gregory Davidson, University of Michigan

Wachspress (1975) determined that certain rational functions perform well as basis functions in finite element methods (FEM). Adams (2001) theorized that Wachspress rational basis functions should provide a robust discretization in the thick diffusive limit, but his analysis did not provide numerical results of Wachspress rational function discretizations.

In this study, we derive a discontinuous finite element discretization using Wachspress rational basis functions on convex quadrilaterals. We then accelerate this scheme with an Asymptotic-P1 diffusion synthetic acceleration preconditioner. This scheme is then analyzed in the interior for the thick diffusive limit on both orthogonal and skewed logically rectangular meshes.

Theoretical and computational results indicate that Wachspress rational functions provide a robust spatial discretization in the thick diffusive limit.

Abstract Author(s): Gregory G. Davidson, Todd S. Palmer