Thursday, February 16, 9:30 am in room MTH 3206, University of Maryland,
College Park
Countably Normed Spaces and Their Application to Approximation
for Elliptic Problems over Nonsmooth Domains in R^3
Prof. Benqi Guo
Department of Applied Mathematic
University of Manitoba, Canada
bguo@newton.amath.umanitoba.ca
The countably normed space is one of the most effective tools to describe
the singularity of solution for elliptic problems on nonsmmooth domains. The
countably normed spaces in three dimensions with weighted Sobolev norms and
weighted continuous function norms will be addressed, the strctures and their
relations with usual Sobolev spaces of fractional order and continuous function
spaces will be discussed.
The approximability of the functions in these countably normed spaces by
piecewise polynomials is analyzed. The geometric meshes and P-Q distributions
of polynomials are designed in order to achieve the best approximation and
efficiency of the computation, which lead to the exponential convergence of the
h-p version of the finite element method in three dimensions.
|
