四边形外模数的计算
Computation of exterior moduli of quadrilaterals
AI总结：
通过将四边形外模数问题转化为拉普拉斯方程的Dirichlet-Neumann问题，采用hp-FEM算法进行数值求解，并验证了指数收敛性。
摘要：
我们研究了计算有界四边形外模数的问题。将该问题简化为拉普拉斯方程的Dirichlet-Neumann问题的数值解。报告了几个带有误差估计的实验结果。我们的主要方法使用了$hp$-FEM算法，该算法能够在复杂几何情况下进行计算。对于简单几何，观察到与基于SC Toolbox的计算结果良好吻合。我们还使用了我们早期论文中引入的互逆误差估计方法来验证我们的数值结果。特别地，根据Babu\vska和Guo的理论，证明了指数收敛性。
英文摘要：
We study the problem of computing the exterior modulus of a bounded quadrilateral. We reduce this problem to the numerical solution of the Dirichlet-Neumann problem for the Laplace equation. Several experimental results, with error estimates, are reported. Our main method makes use of an $hp$-FEM algorithm, which enables computations in the case of complicated geometry. For simple geometries, good agreement with computational results based on the SC Toolbox, is observed. We also use the reciprocal error estimation method introduced in our earlier paper to validate our numerical results. In particular, exponential convergence, in accordance with the theory of Babu\vska and Guo, is demonstrated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
