Alexandre Madureira
Coordenacao de Matematica Aplicada e Computacional - CMA
Laboratorio Nacional de Computacao Cientifica (LNCC)
A Finite Element Method of Multiscale Type: Basic Ideas and
Applications
In this talk, we will present the basic ideas behind a multiscale finite
element method, and we will consider problems where these ideas were
applied.
In opposition to the traditional finite element method, the multiscale
finite element method looks for solutions of multiscale problems in spaces
enriched with local (elementwise) solutions of the original problem. This was successfully applied to models in composite materials, and
provides a way to circumvent the traditional homogenization procedure.
We will show a new methodology to treat reaction-diffusion problem, in a
reaction dominated regime, coming up with a new finite element method of
Petrov-Galerkin type. This was done in collaboration with Leo Franca,
Fred Valentin, and Lutz Tobiska.
