A posteriori error estimation and adaptive mesh-refinement techniques
A posteriori error estimation and adaptive mesh-refinement techniques
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DOI：
10.1016/0377-0427(94)90290-9
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发表时间：
1994-05
影响因子：
2.4
通讯作者：
R. Verfürth
中科院分区：
文献类型：
--
作者：
R. Verfürth
本文分析了椭圆型偏微分方程三种不同的后验误差估计。它们是基于评价当地的残差相对于强形式的微分方程，在解决当地的问题与诺依曼边界条件，并在解决当地的问题与狄利克雷边界条件。我们证明了这三个是等价的，并产生全局上界和局部下界的真实错误。因此，自适应网格细化技术的基础上，这些估计是能够检测局部奇异的解决方案，并适当地细化这些奇异点附近的网格。一些数值例子证明了误差估计和网格加密技术的有效性。
We analyse three different a posteriori error estimators for elliptic partial differential equations. They are based on the evaluation of local residuals with respect to the strong form of the differential equation, on the solution of local problems with Neumann boundary conditions, and on the solution of local problems with Dirichlet boundary conditions. We prove that all three are equivalent and yield global upper and local lower bounds for the true error. Thus adaptive mesh-refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities. Some numerical examples prove the efficiency of the error estimators and the mesh-refinement techniques.