Algebraic convergence for anisotropic edge elements in polyhedral domains
Algebraic convergence for anisotropic edge elements in polyhedral domains
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DOI：
10.1007/s00211-005-0607-4
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发表时间：
2005-07
影响因子：
2.1
通讯作者：
A. Buffa;M. Costabel;M. Dauge
中科院分区：
文献类型：
--
作者：
A. Buffa;M. Costabel;M. Dauge
本文研究了H型Nédélec边元在多面体各向异性网格上的逼近误差。四面体和六面体元素被认为是，重点是获得最佳的收敛速度在H（旋度）规范的高阶元素。给出了两类估计：第一类是各向异性加权Sobolev空间中函数的插值误差估计.这里我们不仅考虑H（curl）-协调的Nédélec元，而且考虑H（div）-协调的Raviart-Thomas元，它们自然地出现在de Rham复形的离散形式中。我们的技术是通过高度各向异性的坐标变换从参考元素到物理元素的误差估计。第二，时谐麦克斯韦方程组标准H（旋度）近似的Galerkin误差估计。在这里，我们使用各向异性加权Sobolev正则性的解决方案的三维边缘和角落的域。我们还证明了离散紧性所需的麦克斯韦特征值问题的收敛性。我们的结果推广了[40]的结果到多面体角和高阶元的情形。
We study approximation errors for theh-version of Nédélec edge elements on anisotropically refined meshes in polyhedra. Both tetrahedral and hexahedral elements are considered, and the emphasis is on obtaining optimal convergence rates in the H(curl) norm for higher order elements. Two types of estimates are presented: First,interpolationerror estimates for functions in anisotropic weighted Sobolev spaces. Here we consider not only the H(curl)-conforming Nédélec elements, but also the H(div)-conforming Raviart-Thomas elements which appear naturally in the discrete version of the de Rham complex. Our technique is to transport error estimates from the reference element to the physical element via highly anisotropic coordinate transformations. Second,Galerkinerror estimates for the standard H(curl) approximation of time harmonic Maxwell equations. Here we use the anisotropic weighted Sobolev regularity of the solution on domains with three-dimensional edges and corners. We also prove the discrete compactness property needed for the convergence of the Maxwell eigenvalue problem. Our results generalize those of [40] to the case of polyhedral corners and higher order elements.