一个低阶各向异性有限元的超收敛分析

基金项目: 国家自然科学基金资助项目(10371113;10471133;10590353)

Superconvergence Analysis of a Lower Order Anisotropic Finite Element

摘要: 针对二阶椭圆问题,在各向异性网格上得到了由Park和Sheen提出的一个低阶非协调单元的收敛性分析,并给出了相应的误差估计．进一步利用插值后处理技巧,得到了后处理后的离散解与真解本身的整体超收敛性质．最后的数值试验验证了理论的可靠性．
- 非协调有限元 /
- 各向异性 /
- 误差估计 /
- 插值后处理 /
- 超收敛
Abstract: The convergence analysis of the lower order nonconforming element proposed by Park and Sheen was applied to the second order elliptic problem under anisotropic meshes.And the corresponding error estimation was obtained.Moreover,by using the interpolation postprocessing technique,a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself was derived.Numerical results were also given to verify the theoretical analysis.
- nonconforming finite element /
- anisotropic /
- error estimate /
- interpolation postprocessing /
- superconvergence

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