PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Introduction to corner singularities: a priori estimates, the finite element method, and the multigrid method
Seminar:CCMA Luncheon Seminar
Speaker:Hengguang Li (PSU)
Abstract:
It is well known that the solution of an elliptic equation has singularities on non-smooth domains and when the boundary condition changes. This talk is to provide a systematic introduction to singular solutions of this type and to problems that may rise both theoretically and numerically. In stead of usual Sobolev spaces, we will concentrate on the well-posedness and regularity property of the solution in weighted Sobolev spaces, which captures the behavior of the solution well. A general construction of a sequence of finite element spaces will be presented accordingly to recover the quasi-optimal rate of convergence of the numerical solution. In addition, based on the method of subspace corrections, a convergence estimate will show the optimality of the multigrid method on these special subspaces. An interesting software package for handling singular solutions will be introduced at the end.

Room Reservation Information

Room Number:MB114
Date:09 / 14 / 2007
Time:12:15pm - 01:25pm