A posteriori error estimates with post-processing for nonconforming finite elements
A posteriori error estimates with post-processing for nonconforming finite elements
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DOI：
10.1051/m2an:2002022
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发表时间：
2002-05
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影响因子：
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通讯作者：
F. Schieweck
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文献类型：
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作者：
F. Schieweck
对于椭圆模型问题的非线性有限元逼近，我们提出了能量范数的后验误差估计，它将原非线性有限元解和该解的一个易于计算的一致逼近之间的“后处理误差”作为一个附加项.因此，对于误差分析，现有的理论，从符合的情况下，可以使用一些简单的额外的参数。作为一个基本点，利用的性质，该有限元素空间包含作为子空间的一个协调的有限元空间的一阶。这一性质在许多已知的非线性空间中得到了满足。我们证明了局部较低和全球上后验误差估计的增强的误差测量，这是离散能量范数的离散化误差加上误差的最佳表示的精确解的一个功能，在符合空间用于后处理。我们证明，使用计算一致的近似的ESTA解决方案的想法也可以适用于推导出一个后验误差估计的线性泛函的解决方案，它代表了一些物理利益。
For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited that the nonconforming finite element space contains as a subspace a conforming finite element space of first order. This property is fulfilled for many known nonconforming spaces. We prove local lower and global upper a posteriori error estimates for an enhanced error measure which is the discretization error in the discrete energy norm plus the error of the best representation of the exact solution by a function in the conforming space used for the post-processing. We demonstrate that the idea to use a computed conforming approximation of the nonconforming solution can be applied also to derive an a posteriori error estimate for a linear functional of the solution which represents some quantity of physical interest.