Natural superconvergence points in three-dimensional finite elements

被引：44
作者：
Lin, Runchang [1 ]
Zhang, Zhimin [2 ]
机构：
[1] Texas A&M Int Univ, Dept Math & Phys Sci, Laredo, TX 78041 USA
[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 03期
关键词：
finite element methods; natural superconvergence; hexahedral; pentahedral (triangular prism); tetrahedral elements polynomial;
D O I：
10.1137/070681168
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C(0) finite elements in a three-dimensional setting. This identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces. Derivative and function value superconvergence points are investigated for both the Poisson and the Laplace equations. Superconvergence results are reported for hexahedral, pentahedral, and tetrahedral elements up to certain degrees.
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页码：1281 / 1297
页数：17
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