Numerical Boundary Corrector For Elliptic Equations with Rapidly Oscillating Periodic Coefficients
Finite elements | homogenization | elliptic equations | multiscaling | boundary layer | mixed finite elements
We develop a numerical discretization for linear elliptic equations with rapidly oscillating coefficients. The major goal in this paper is to develop a numerical approximation scheme on a mesh size $h>\epsilon$ (or $h>>\epsilon$) with quasi-optimal approximation on $L^2$ and broken $H^1$ norms. The new method is based on asymptotic analysis and a careful treatment of the boundary corrector term. This kind of equation has applications in areas such as on the study of flow through porous media and composite materials.