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.

我们提出了一种用于自伴随线性椭圆特征值问题的高阶p或hp有限元离散化的后验误差估计器，适用于估计特征值簇和相应不变子空间的近似误差。估计器基于近似误差函数的计算，该空间与计算近似特征向量的空间互补。这些误差函数用于构建误差集体度量的估计值，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间隙。数值实验证明了该方法的实际有效性。