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Derivative superconvergent points
in finite element solutions of Poisson's equation
for the serendipity and intermediate families
- a theoretical justification

Author: Zhimin Zhang
Journal: Math. Comp. 67 (1998), 541-552
MSC (1991): Primary 65N30
MathSciNet review: 1459393
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Abstract | References | Similar Articles | Additional Information

Abstract: Finite element derivative superconvergent points for the Poisson equation under local rectangular mesh (in the two dimensional case) and local brick mesh (in the three dimensional situation) are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In case of the serendipity family, the results are given for finite element spaces of order below 7. Any finite element space that contains the complete polynomial space will have at least all superconvergent points of the related serendipity family.

References [Enhancements On Off] (What's this?)

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Additional Information

Zhimin Zhang
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409

Received by editor(s): May 29, 1996
Additional Notes: This work was supported in part by NSF Grants DMS-9626193 and DMS-9622690.
Article copyright: © Copyright 1998 American Mathematical Society