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Report 1999-08
Approximation on Simplices with respect to Weighted Sobolev Norms
D. Braess and C. Schwab
Abstract: Inequalities of Jackson and Bernstein type are derived for polynomial approximation on simplices with respect to Sobolev norms. Although we cannot use orthogonal polynomials, sharp estimates are obtained from a decomposition into orthogonal subspaces. The formulas reflect the symmetries of simplices, but comparable estimates on rectangles show that we cannot expect rotational invariance of the terms with derivatives.
Paper: Available as PDF (165 KB) or as hardcopy to order reports@sam.math.ethz.ch.
Publishing information: to appear in Journal of Approx. Theory
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