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math.NA2015★ 2 cited
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient
Thomas Y. Hou, Pengfei Liu
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to co…
math.NA2014★ 14 cited
A Heterogeneous Stochastic FEM Framework for Elliptic PDEs
Thomas Y. Hou, Pengfei Liu
We introduce a new concept of sparsity for the stochastic elliptic operator , which reflects the compactness of its inverse operator in…