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

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

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 projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.

  • Keywords

Interpolation operator of projection type, Finite element, Superconvergence.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-277, author = {Zhang , TieLin , Yan-Ping and Tait , R. J.}, 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 projections, which are also the finite element 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 AU - Zhang , Tie AU - Lin , Yan-Ping AU - Tait , R. J. 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, Finite element, 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 projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.

Zhang , TieLin , Yan-Ping and Tait , R. J.. (2002). Superapproximation Properties of the Interpolation Operator of Projection Type and Applications. Journal of Computational Mathematics. 20 (3). 277-288. doi:
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