Volume 20, Issue 3
Superapproximation Properties of the Interpolation Operator of Projection Type and Applications

Tie Zhang, Yan Ping Lin & R. J. Tait

DOI:

J. Comp. Math., 20 (2002), pp. 277-288

Published online: 2002-06

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  • Abstract

Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both prjections, which are also the finite slement approximation solutions of the elliptic problems and the Sobolev equations, respectively.

  • Keywords

Interpolation operator of projection type Finite element Superconvergence

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@Article{JCM-20-277, author = {}, title = {Superapproximation Properties of the Interpolation Operator of Projection Type and Applications}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {3}, pages = {277--288}, abstract = { Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both prjections, which are also the finite slement approximation solutions of the elliptic problems and the Sobolev equations, respectively. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8917.html} }
TY - JOUR T1 - Superapproximation Properties of the Interpolation Operator of Projection Type and Applications JO - Journal of Computational Mathematics VL - 3 SP - 277 EP - 288 PY - 2002 DA - 2002/06 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8917.html KW - Interpolation operator of projection type KW - Finite element KW - Superconvergence AB - Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both prjections, which are also the finite slement approximation solutions of the elliptic problems and the Sobolev equations, respectively.
Tie Zhang, Yan Ping Lin & R. J. Tait. (1970). Superapproximation Properties of the Interpolation Operator of Projection Type and Applications. Journal of Computational Mathematics. 20 (3). 277-288. doi:
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