An Interior Estimate of Superconvergence for Finite Element Solutions for Second-Order Elliptic Problems on Quasi-uniform Meshes by Local Projections
An Interior Estimate of Superconvergence for Finite Element Solutions for Second-Order Elliptic Problems on Quasi-uniform Meshes by Local Projections
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DOI：
10.1137/s0036142902410039
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发表时间：
2003-04
期刊：
影响因子：
--
通讯作者：
Hongsen Chen;Junping Wang
中科院分区：
文献类型：
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作者：
Hongsen Chen;Junping Wang
利用投影法建立了二阶椭圆型问题有限元解的超收敛估计，该估计仅依赖于区域的局部性质和有限元解。投影法是一种利用最小二乘法构造新的近似的后处理过程。特别地，对于Galerkin有限元解的局部投影，导出了L2范数和$L^\infty$范数下的一些局部超收敛估计。研究结果有两个突出特点。首先，建立了在科学计算中具有实际意义的拟均匀网格。其次，根据区域的局部性质和二阶椭圆型问题的解，导出了它们。因此，本文的结果可用于实际计算中提供有用的后验误差估计。
This paper establishes some superconvergence estimates for finite element solutions of second-order elliptic problems by a projection method depending only on local properties of the domain and the finite element solution. The projection method is a postprocessing procedure that constructs a new approximation by using the method of least squares. In particular, some local superconvergence estimates in the L2 and $L^\infty$ norms are derived for the local projections of the Galerkin finite element solution. The results have two prominent features. First, they are established for any quasi-uniform meshes, which are of practicalimportance in scientific computation. Second, they are derived on the basis of local properties of the domain and the solution for the second-order elliptic problem. Therefore, the result of this paper can be employed to provide useful a posteriori error estimators in practical computing.