Students are welcome to communicate with each other and the teacher on-line using the Web page
http://www-math.cudenver.edu/~aknyazev/teaching/98/7664/comments
Project Description:
We consider a parametric family of homogeneous Dirichlet
boundary value problems for the diffusion
equation
-div( k grad u)=f
with the diffusion coefficient k=k(x) equal to a small constant, our
parameter, in a
subdomain. Such problems are not uniformly well-posed when the parameter gets
small.
We investigate numerically FEM accuracy in the
standard parameter-independent Sobolev norm. We consider a traditional FEM
with the only additional assumption that the boundary of the subdomain with
the small coefficient does not cut any finite element.
Our goal is to look into dependence of the FEM error
on the parameter under assumption that the solution
is piecewise smooth. We consider three model problems:
a square divided into 2 rectangles, a square divided into
4 squares, and an L-shaped domain divided into 2 rectangles.
The Report in HTML and PostScript forms.
Numerical results of the project were included
in the paper:
A. V. Knyazev and Olof Widlund,
Lavrentiev Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for
Differential Equations with Rough Coefficients,
Submitted to Mathematics of Computation. Published as a technical report
UCD-CCM 132, 1998, at the Center for Computational Mathematics, University of Colorado at Denver.