Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions (Communications in Computational Physics, 2009)
We study the multiscale finite element method for solving multiscale ellipticproblems with highly oscillating coefficients, which is designed to accurately capturethe large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differentialequation with proper boundary conditions. The boundary conditions are chosen to extract more accurate boundary information in the local problem. We consider periodicand non-periodic coefficients with linear and oscillatory boundary conditions for thebase functions. Numerical examples will be provided to demonstrate the effectivenessof the proposed multiscale finite element method.