An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems

Abstract

We present a novel adaptive higher-order finite element (hp-FEM) algorithm to solve non-symmetric elliptic eigenvalue problems. This is an extension of our prior work on symmetric elliptic eigenvalue problems. The method only needs to make one call to a generalized eigensolver on the coarse mesh, and then it employs Newton’s or Picard’s methods to resolve adaptively a selected eigenvalue–eigenvector pair. The fact that the method does not need to make repeated calls to a generalized eigensolver not only makes it very efficient, but it also eliminates problems that pose great complications to adaptive algorithms, such as eigenvalue reordering or returning arbitrary linear combinations of eigenvectors associated with the same eigenvalue. New theoretical and numerical results for the non-symmetric case are presented.