Devising Efficient HDG Methods for Diffusion Problems

Event Sponsor: 
Mathematics and Computing Science Seminar
Start Date: 
Jan 22 2016 - 10:30am
Building/Room: 
Building 240/Room 1404-1405
Location: 
Argonne National Laboratory
Speaker(s): 
Guosheng Fu
Speaker(s) Title: 
University of Minnesota
Host: 
Sven Leyffer

We present an HDG formulation for a model Possion's equation on a polygonal/polyhedral mesh. We then discuss two approaches to devise HDG methods with optimal convergence (or superconvergence) property. The first approach is to suitably choose the stabilization function (or the penalty term) to get optimality. (This idea was originally presented in Christoph Lehrenfeld's Diploma Thesis [2010] under the direction of Joachim Schoberl) The second approach is to systematically modify (or augment) the approximation spaces in a suitable way such that the projection based error analysis [Mathematics of Computation 79 (271), 1351 1367] can be applied. (It is the continuation of the work started [Mathematics of Computation 79 (271), 1351-1367] on searching for "superconvergent" HDG methods) Preliminary numerical results on polygonal meshes are presented.