A posteriori error estimation for the dual mixed finite element method for the p-Laplacian in a polygonal domain
A posteriori error estimation for the dual mixed finite element method for the p-Laplacian in a polygonal domain
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DOI：
10.1016/j.cma.2006.11.023
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发表时间：
2007-05
影响因子：
7.2
通讯作者：
E. Creusé;M. Farhloul;L. Paquet
中科院分区：
文献类型：
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作者：
E. Creusé;M. Farhloul;L. Paquet
对于p-Laplace方程的对偶混合形式的离散解，我们定义了两个留数R和r。然后，我们根据这两个剩余的范数来约束这两个未知数的误差范数。然后，我们用两个误差估计量的函数来约束这两个残差的范数，这两个误差估计量的表达式最多只包含数据和计算量。接下来，我们解释如何杂交和解决离散化的对偶混合公式。最后，我们首先通过p=1.8和p=3的数值试验来证实Farhloul和Manouzi [M. Farhloul，H. Manouzi，关于p-Laplacian的混合有限元方法，加拿大应用数学季刊8（2000）67-78]，第二，实验验证我们的后验误差估计的可靠性。
For the discrete solution of the dual mixed formulation for the p-Laplace equation, we define two residues R and r. Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next explain how the discretized dual mixed formulation is hybridized and solved. We close our paper by numerical tests for p=1.8 and p=3 firstly to corroborate the orders of convergence established by Farhloul and Manouzi [M. Farhloul, H. Manouzi, On a mixed finite element method for the p-Laplacian, Canadian Applied Mathematics Quarterly 8 (2000) 67–78], and secondly to experimentally verify the reliability of our a posteriori error estimates.