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Approximation on Simplices with respect to Weighted Sobolev Norms

by D. Braess and Ch. Schwab

(Report number 1999-08)

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.

Keywords:

@Techreport{BS99_243,
  author = {D. Braess and Ch. Schwab},
  title = {Approximation on Simplices with respect to Weighted Sobolev Norms},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-08},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-08.pdf },
  year = {1999}
}

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