Numerical Analysis and Scientific Computing Seminar

Non-conforming Finite Element Methods for the Brinkman Problem and a Singularly Perturbed Fourth-order Problem

Speaker: Johnny Guzman, Brown University

Location: Warren Weaver Hall 1302

Date: Sept. 30, 2011, 10 a.m.

Synopsis:

We show that one can augment H(div) elements (e.g. Raviart-Thomas elements) with divergence free functions to construct stable methods for the Brinkman problem. The resulting methods are H(div) conforming, but are H1 non-conforming. Using exact sequences of function spaces we also obtain non-conforming H2 elements that we use to solve singularly perturbed fourth order problems. This is joint work with Michael Nelian (UPitt) and Dmitriy Leykekhman (UConn).