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Steklov Approximations of Harmonic Boundary Value Problems on Planar Regions (1609.07400v1)
Published 23 Sep 2016 in math.AP
Abstract: Error estimates for approximations of harmonic functions on planar regions by subspaces spanned by the first harmonic Steklov eigenfunctions are found. They are based on the explicit representation of harmonic functions in terms of these harmonic Steklov eigenfunctions. When the region is a rectangle of aspect ratio h, some computational results regarding these approximations for problems with known explicit solutions are described.
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