A Posteriori Error Estimation of a Stabilized Mixed Finite Element Method for Darcy Flow
A Posteriori Error Estimation of a Stabilized Mixed Finite Element Method for Darcy Flow
复制标题
达西流稳定混合有限元法的后验误差估计
DOI：
10.1007/978-3-319-25727-3_2
复制
发表时间：
2015
影响因子：
2.1
通讯作者：
María González
中科院分区：
文献类型：
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作者：
T. Barrios;J. M. Cascón;María González
我们考虑Barrios等人（computational Methods applied Mech Eng 283:909-922, 2015）提出的扩展混合有限元法来计算达西流。考虑到诺伊曼边界条件的近似，我们进行了先验和后验误差分析。我们推导了一个后验误差指标，它由内部元素上的两个残差项和边界元素上边界条件误差的附加项组成。我们证明了误差指示器在内部元素上是可靠和局部有效的。数值实验证明了该自适应算法的良好性能。
We consider the augmented mixed finite element method proposed in Barrios et al. (Comput Methods Appl Mech Eng 283:909–922, 2015) for Darcy flow. We develop the a priori and a posteriori error analyses taking into account the approximation of the Neumann boundary condition. We derive an a posteriori error indicator that consists of two residual terms on interior elements and an additional term that accounts for the error in the boundary condition on boundary elements. We prove that the error indicator is reliable and locally efficient on interior elements. Numerical experiments illustrate the good performance of the adaptive algorithm.