An Adaptive Surface Finite Element Method Based on Volume Meshes
An Adaptive Surface Finite Element Method Based on Volume Meshes
复制标题
基于体网格的自适应曲面有限元方法
DOI：
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发表时间：
2012
影响因子：
2.9
通讯作者：
M. Olshanskii
中科院分区：
文献类型：
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作者：
A. Demlow;M. Olshanskii
在本文中，我们定义了一个自适应版本的最近推出的有限元方法的数值处理椭圆型偏微分方程定义在表面上。该方法使用（标准）外部体积网格来离散嵌入$mathbb{R}^3 $中的二维曲面上的方程。避免了方程从表面的延伸，但是自由度（d.o.f.）是最佳的，因为它与直接对曲面进行网格化的方法相当。在以前的工作中，它被证明，该方法具有最佳的收敛阶的椭圆曲面偏微分方程，如果体积网格是均匀细化。在本文中，我们扩展的方法，并开发了一个后验误差分析，承认自适应细化网格。本文证明了一种残差型后验误差估计的可靠性，并通过一系列的实验对该估计的可靠性和有效性进行了数值研究。一个简单的自适应细化策略的基础上的误差估计数值…
In this paper we define an adaptive version of a recently introduced finite element method for numerical treatment of elliptic PDEs defined on surfaces. The method makes use of a (standard) outer volume mesh to discretize an equation on a two-dimensional surface embedded in $mathbb{R}^3$. Extension of the equation from the surface is avoided, but the number of degrees of freedom (d.o.f.) is optimal in the sense that it is comparable to methods in which the surface is meshed directly. In previous work it was proved that the method exhibits optimal order of convergence for an elliptic surface PDE if the volume mesh is uniformly refined. In this paper we extend the method and develop an a posteriori error analysis which admits adaptively refined meshes. The reliability of a residual type a posteriori error estimator is proved and both reliability and efficiency of the estimator are studied numerically in a series of experiments. A simple adaptive refinement strategy based on the error estimator is numerical...