Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Residual Error Estimate for Bem-based Fem on Polygonal Meshes Residual Error Estimate for Bem-based Fem on Polygonal Meshes Residual Error Estimate for Bem-based Fem on Polygonal Meshes
Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Residual Error Estimate for Bem-based Fem on Polygonal Meshes Residual Error Estimate for Bem-based Fem on Polygonal Meshes Residual Error Estimate for Bem-based Fem on Polygonal Meshes
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Universität Des Saarlandes Fachrichtung 6.1 – 多边形网格上基于 Bem 的有限元的数学残余误差估计 多边形网格上基于 Bem 的有限元的残余误差估计 多边形网格上基于 Bem 的有限元的残余误差估计
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通讯作者：
Steffen Weißer
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作者：
Steffen Weißer
介绍了一种自然处理悬挂节点的多边形网格协调有限元方法。定义了满足局部齐次偏微分方程的无偏函数，并利用局部边界积分方程进行处理。利用Clément型拟插值算子得到了基于残差的误差估计。这种后验估计器可用于评价多边形单元上的近似精度，或者可应用于基于自适应边界元的有限元。数值实验证实了我们的结果，并显示了一般网格上的自适应策略的最优收敛性。
A conforming finite element method on polygonal meshes is introduced which handles hanging nodes naturally. Ansatz functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clément type a residual-based error estimate is obtained. This a posteri-ori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive BEM-based FEM. The numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes.