Approximation on Simplices with Respect to Weighted Sobolev Norms

✍ Scribed by Dietrich Braess; Christoph Schwab

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 120 KB
• Volume: 103
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1999.3429

✦ Synopsis

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 analogous estimates on rectangles show that we cannot expect rotational invariance of the terms with derivatives.