论文标题
基于投影错误的确保L2误差界限的Laplace本征函数的有限元近似值
Projection error-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions
论文作者
论文摘要
为了符合拉普拉斯特征函数的有限元近似，提出了完全可计算的保证误差，以$ l^2 $ norm sense绑定。结合基于符合有限元方法的盖金投影的先验误差估计，并且具有最差的规律性的特征函数的最佳收敛速度。所产生的误差估计范围是精确和近似本征函数的空间的距离，因此即使在多个和紧密聚集的特征值的情况下，也是可靠的。通过数值示例说明了所提出的结合的准确性。演示代码可在https://ganjin.online/xfliu/eigenfunctionEstimatimatimation4fem上获得。
For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the $L^2$ norm sense is proposed. The bound is based on the a priori error estimate for the Galerkin projection of the conforming finite element method, and has an optimal speed of convergence for the eigenfunctions with the worst regularity. The resulting error estimate bounds the distance of spaces of exact and approximate eigenfunctions and, hence, is robust even in the case of multiple and tightly clustered eigenvalues. The accuracy of the proposed bound is illustrated by numerical examples. The demonstration code is available at https://ganjin.online/xfliu/EigenfunctionEstimation4FEM .
