Sesión Análisis Numérico y OptimizaciónDiscretization reduction for elliptic problems with rough coefficients
Marcus Sarkis
Worcester Polytechnic Institute , USA - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
Abstract: We consider multiscale finite element methods to approximate the solution of an elliptic partial differential equation with rough coefficients. The methods follow the Variational Multiscale and the Localized Orthogonal Decomposition–LOD methods and the adaptive domain decomposition method denoted by BDDC-Balancing Domain Decomposition with Constraints in order to select local modes based on localized generalized eigenvalue problems. On the first stage of the proposed method, the degrees of freedom of the multiscale basis functions are based on the corners of a coarse triangulation, and on the second stage modes on the edges of coarse triangulation are chosen based on these local generalized eigenvalue problems. As a result, optimal error energy estimate is achieved which is mesh and coefficient independent and with localized multiscale functions, and without assuming any regularity of the solution beyond the H1 norm. Numerical experiments are provided. This is a joint work with Alexandre Madureira, LNCC, Brazil.
Trabajo en conjunto con: Alexandre Madureira (Laboratorio Nacional de Computacao Cientifica- LNCC, Brazil).
Referencias
[1] Spectral ACMS: A Robust Localized Approximated Component Mode Synthesis Method, Alexandre Madureira and Marcus Sarkis, SIAM Journal on Numerical Analysis 63 (3), 1055-1077
[2] Hybrid localized spectral decomposition for multiscale problems Alexandre Madureira and Marcus Sarkis SIAM Journal on Numerical Analysis 59 (2), 829-863