论文标题
使用辅助子空间技术的椭圆特征值问题的后验错误估计
A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
论文作者
论文摘要
我们提出了一个高阶$ p $ - 或$ hp $ - $ hp $的后验误差估计器的自我接触线性线性椭圆特征问题，该问题适用于估计特征值群集近似和相应的不敞开式subpace的近似值中的误差。该估计器基于对近似特征向量的空间中近似误差函数的计算。这些误差函数用于构建误差的集体度量估计值，例如特征值的真实和近似簇之间的Hausdorff距离，以及相应的真实和近似不变子空间之间的子空间差距。数值实验证明了该方法的实际有效性。
We propose an a posteriori error estimator for high-order $p$- or $hp$-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate invariant subspaces. Numerical experiments demonstrate the practical effectivity of the approach.
