| SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS |
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| 作者姓名： | Tie Zhang |
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| 作者单位： | Tie Zhang (Department of Mathematics，Northeastern University，Shenyang 110006，China)Yan-ping Lin R.J. Tait (Department of Mathematical Sciences，University of Alberta，Canada，T6G 2G1) |
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| 基金项目： | Supported by the Foundation of National Education Department for Key Teachers in Chinese University. |
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| 摘 要： | AbstractSome 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.
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SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS |
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| Tie Zhang.SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS[J].Journal of Computational Mathematics,2002(3). |
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| Authors: | Tie Zhang |
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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. |
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| Keywords: | Interpolation operator of projection type Finite element Superconvergence |
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