Abstract:
Multiscale (i.e., ``generalized'') finite elements were
introduced by Babuška and Osborn in the 1980's, and they have seen
a reemergence for handling problems with fine-scale heterogeneities.
The method involves solving the overall partial differential equation
on a course grid by incorporating microstructure directly into the
finite element basis. This is accomplished by solving local or
subgrid problems that resolve the microstructure. We consider a
second order elliptic problem in mixed form, and formulate the ideas
as a variational multiscale method. We show the relation of this
method to multiscale finite elements, prove various a priori error
estimates, and present various numerical results.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.