Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh‐refinement
Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh‐refinement
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基于各向同性网格细化的弱奇异积分方程自适应 3D BEM 的收敛性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
D. Praetorius
中科院分区：
文献类型：
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作者：
M. Karkulik;G. Of;D. Praetorius
考虑了三维Laplacian弱奇异积分方程的基于各向同性网格加密的自适应最低阶边界元方法。该方案解决了两个，可能的奇异性的解决方案，以及给定的数据。因此，该实现仅处理离散积分算子，即矩阵。我们证明，通常的自适应网格细化算法驱动相应的误差估计为零。在一个适当的饱和假设下，这是经验观察，离散的解决方案的序列，从而趋于精确的解决方案内的能量范数。© 2013威利期刊公司. Numer Methods Partial Differential Eq，2013
We consider the adaptive lowest‐order boundary element method based on isotropic mesh refinement for the weakly‐singular integral equation for the three‐dimensional Laplacian. The proposed scheme resolves both, possible singularities of the solution as well as of the given data. The implementation thus only deals with discrete integral operators, that is, matrices. We prove that the usual adaptive mesh‐refining algorithm drives the corresponding error estimator to zero. Under an appropriate saturation assumption which is observed empirically, the sequence of discrete solutions thus tends to the exact solution within the energy norm. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013