The University of Arizona

Mixed finite element methods for second order elliptic problems

Mixed finite element methods for second order elliptic problems

Series: Program in Applied Mathematics Colloquium
Location: Math 402
Presenter: Todd Arbogast, Department of Mathematics, University of Texas, Austin

Second order elliptic equations -div(a grad p) = f can be solved approximately for the scalar variable p directly.  However the vector flux u = -a grad p is often the variable of interest. Mixed methods write the equation as a system of first order equations for p and u.  Finite element solution provides accurate approximation of both variables.  We describe the basic theory of mixed methods, including the need for an inf-sup condition and implementation in the hybrid form.  We review existing families of mixed finite elements and discuss new families of finite elements that work well on quadrilaterals and cuboidal hexahedra. To show the richness of mixed method approaches, we then discuss several applications, including two-phase flow in a porous medium, variational multiscale techniques (i.e., multiscale finite elements), multiscale mortar methods, and mantle dynamics.

Department of Mathematics, The University of Arizona 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089 USA Voice: (520) 621-6892 Fax: (520) 621-8322 Contact Us © Copyright 2017 Arizona Board of Regents All rights reserved