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About SIAM
The Society for Industrial and Applied Mathematics (SIAM) aims to advance the application of mathematics and computational science to engineering, industry, science, and society.

About the Chapter
The SIAM student chapter at the University of Illinois at Urbana-Champaign was created in the fall of 2006, is supported by the SIAM parent organization, and is a registered student organization at UIUC.

UIUC SIAM Student Chapter Colloquium

Prof. Chad Westphal, Wabash College

"Least-Squares Finite Element Methods for Partial Differential Equations in Nonsmooth Domains"

Logistics

  • Thursday 11/13/08 at 4PM
  • Siebel Center 4405

Abstract

Partial differential equations posed on polygonal/polyhedral domains may have
nonsmooth solutions near the corners, and numerical methods to approximate these
solutions may suffer as a consequence. Global reduction of discretization
convergence rates or even loss of convergence can occur. In this talk, we'll
discuss a specific approach to combat this within the least-squares finite element
context. By replacing the standard Sobolev norms in a least-squares functional
with appropriately weighted norms, we are able to eliminate the the global
"pollution effect" caused by the nonsmooth solution and recover better (often
optimal) rates of convergence in both weighted and nonweighted norms. Examples are
given in both div-curl and H(div) settings as well as extensions to applications in
fluid mechanics.

Pictures from the talk


Contact
Our postal address:

SIAM
Siebel Center for Computer Science
University of Illinois at Urbana-Champaign
201 N. Goodwin Ave.
Urbana, IL 61801

Our email: siam-chapter@illinois.edu



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