PROJECTION METHOD APPLIED TO DIFFUSION IN A PERIODIC STRUCTURE.

Michael Vogelius; George Papanicolaou

doi:10.1137/0142091

PROJECTION METHOD APPLIED TO DIFFUSION IN A PERIODIC STRUCTURE.

Michael Vogelius, George Papanicolaou

Research output: Contribution to journal › Article

9 Scopus citations

Abstract

A method designed to replace PDE's with rapidly varying coefficients by PDE's with constant coefficients is analyzed. This method is based on a combination of an asymptotic expansion and a variational principle. It is shown that for smooth data the method has the same approximation properties as the more standard approach based only on an asymptotic expansion. More important, it is shown that the present method works well also for nonsmooth data. This may be seen as a result of the optimal way in which the method treats boundary layers.

Original language	English (US)
Pages (from-to)	1302-1322
Number of pages	21
Journal	SIAM Journal on Applied Mathematics
Volume	42
Issue number	6
DOIs	https://doi.org/10.1137/0142091
State	Published - Jan 1 1982
Externally published	Yes

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1137/0142091

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Vogelius, M., & Papanicolaou, G. (1982). PROJECTION METHOD APPLIED TO DIFFUSION IN A PERIODIC STRUCTURE. SIAM Journal on Applied Mathematics, 42(6), 1302-1322. https://doi.org/10.1137/0142091

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