正多边形区域上Laplace算子特征值的非结构网络谱元法

An Unstructured Spectral Element Method for the Laplace Eigenvalue Problem on Regular Polygons

采用高精度的混合三角形、四边形单元剖分求解任意正多边形区域上的Laplace算子的特征值.由Legendre多项式线性组合构造内部单元的基函数和边界基函数.首先,给出特征值的误差估计和算法实现.然后,测试数值算例的精度,以验证理论结果,表明方法的有效性及正确性.

In this paper,we use an unstructured spectral element method which mixed triangularand quadrangle for the Laplace eigenvalue problem on the regular polygon domain.We construct the basis functions by combing with the Legendre polynomials for the interior element and boundary.The convergence of the eigenvalue and numerical implement are also given.Finally,a series of numerical examples are provided to support the theoretical results and demonstrate the accuracy and efficiency of this methods.