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A multiscale finite element method for oscillating Neumann problem on rough domain

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.

preprint2016arXivOpen access
P. B. MingX. Xu
math.NA
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Open access2 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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P. B. MingX. Xu

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