The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis
The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis
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DOI：
10.1016/j.apnum.2010.03.012
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发表时间：
2009-05
影响因子：
2.8
通讯作者：
A. Bespalov;N. Heuer
中科院分区：
文献类型：
--
作者：
A. Bespalov;N. Heuer
本文给出了求解分段平面（开或闭）Lipschitz曲面上电场积分方程的hp型边界元法的先验误差分析。我们使用H（div）-符合离散与Raviart-Thomas元素上的一系列准均匀网格的三角形和/或平行四边形。假设电场积分方程解在切向矢量场的Sobolev空间中的正则性，并基于已知的拟最优收敛性，证明了该方法在能量范数下的先验误差估计.该估计证明了关于网格参数h和多项式次数p的预期收敛速度。
This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart–Thomas elements on a sequence of quasi-uniform meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric field integral equation in terms of Sobolev spaces of tangential vector fields, and based upon the known quasi-optimal convergence, we prove an a priori error estimate of the method in the energy norm. This estimate proves the expected rate of convergence with respect to the mesh parameter h and the polynomial degree p.