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DIRECT ESTIMATION FOR MULTIVARIATE POLYNOMIAL APPROXIMATION | ||
| journal of kerbala university | ||
| Article 1, Volume 2, Issue 4, 2006, Pages 137-142 PDF (0 K) | ||
| Authors | ||
| Eman Samir Bhaya; Hussein Ali Mohammed | ||
| Abstract | ||
| The Bramble-Hilbert lemma is a fundamental result on multivariate polynomial approximation .It is frequently applied in the analysis of finite element methods used for numerical solutions. Our main result is to improve the following Bramble-Hilbert lemma to the case :let be abounded convex domain and let , ,0 ,where ( ) is the Sobolev spaces ,then there exists a polynomial P of degree m-1 for which c(n,m)(diam ) g , where . = is the Sobolev semi norm of order . As a consequence we get that for f L , < . c , where , is the rate of polynomial approximation of degree , and is the averaged modulus of smoothness, and >0. | ||
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