Superconvergent two-grid methods for elliptic eigenvalue problems (Q514444)

The authors consider the following second-order self-adjoint elliptic eigenvalue problem \[ \begin{aligned} -\nabla(D\nabla u) + c u &= \lambda u \text{ in }u \Omega,\\ u&=0 \text{ on } \partial \Omega, \tag{1} \end{aligned} \] where \(\Omega\) in \(\mathbb{R}^2\) is a polygonal domain with Lipschitz boundary, \(D\) is a 2\(\times\)2 symmetric positive definite matrix and \(c \in L^\infty(\Omega)\). A new two-grid numerical method to solve (1) is proposed in this work. Its algorithmic implementation is computationally more efficient than some other existing computational approaches and the method posseses superconvergence property. The theoretical results are illustrated by three numerical examples.