A multiscale finite element method for oscillating Neumann problem on rough domain
Numerical Analysis
2016-08-12 v3
Abstract
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the microscopically geometrical and physical information of the rough boundary. We prove the method has optimal convergence rate in the energy norm with a weak resonance term for periodic roughness. Numerical results are reported for both periodic and nonperiodic roughness.
Cite
@article{arxiv.1509.08384,
title = {A multiscale finite element method for oscillating Neumann problem on rough domain},
author = {P. B. Ming and X. Xu},
journal= {arXiv preprint arXiv:1509.08384},
year = {2016}
}