Domain Decomposition Algorithms With Small Overlap

Cover Domain Decomposition Algorithms With Small Overlap
Domain Decomposition Algorithms With Small Overlap
Maksymilian Dryja
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Since u{x, 0) = u(x, y) - J — Q^ — dr, we find, by elementary axguments, that H \u{x, 0)\'dx|2, (n. ) Now consider the integral over a narrow subregion next to one of the sides of the square. Using similar arguments, we obtain (14) j" f^ \u{x, y)\^dxdy (n. ) + 2(f^, ))' as required.
The modifications necessary for the case of an arbitrary, shape regulax substruc- ture and the extension of the proof to the case of three dimensions are routine. D 9 Lemma 4. Let Uh be a continuous, piecewise quadr
...atic function defined on the finite element triangulation and let IhUh G V^ be its piecewise linear interpolant on the same mesh. Then there exists a constant C, independent of h and H, such that UhUhlnHQ. )

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