PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Victor Nistor, Jinchao Xu, Xiantao Li, Yuxi Zheng, Kris Jenssen, Hope Shaffer.

Title:Weighted Norm Least Squares Finite Element Methods for Problems with Singularities
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Chad Westphal, Wabash College
Abstract:
Partial differential equations posed on polygonal/polyhedral domains often have nonsmooth solutions near the corners/edges, and numerical methods to approximate these solutions often suffer as a consequence. Other problems may have singular or degenerate coefficients at points in the interior of the domain, again leading to a locally nonsmooth solution. Depending on the regularity of the original problem, the choice of the variational problem, and the finite element spaces used, global reduction of discretization convergence rates or even a loss of convergence can occur as a result of these singularities. We present a weighted norm least squares minimization approach, where the metric of the approximation space is chosen to balance the components of the error in an optimal way. We give an overview of the motivating analysis and numerical examples for problems with boundary singularities and with singular/degenerate coefficients and and discuss extensions to various applications.

Room Reservation Information

Room Number:MB106
Date:09 / 16 / 2011
Time:03:35pm - 04:25pm