Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient ∗

@inproceedings{Hou2015OptimalLM,
title={Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient ∗},
author={Thomas Y. Hou and Pengfei Liu},
year={2015}
}

This paper addresses a multi-scale finite element method for second order linear elliptic equations with rough coefficients, which is based on the compactness of the solution operator, and does not depend on any scaleseparation or periodicity assumption of the coefficient. We consider a special type of basis functions, the multi-scale basis, which are harmonic on each element and show that they have optimal approximation property for fixed local boundary conditions. To build the optimal local… CONTINUE READING