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http://math.ucdenver.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 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.
We use different iterative methods with different initial
approximations.
Our goal is to look into dependence of the convergence rate
on the parameter
in a standard parameter-independent Sobolev norm.
The Report in HTML and PostScript forms.