An adaptive finite element method with asymptotic saturation for eigenvalue problems

作者：Carstensen C^*; Gedicke J; Mehrmann V; Miedlar A

来源：Numerische Mathematik, 2014, 128(4): 615-634.

DOI：10.1007/s00211-014-0624-2

This paper discusses adaptive finite element methods for the solution of elliptic eigenvalue problems associated with partial differential operators. An adaptive method based on nodal-patch refinement leads to an asymptotic error reduction property for the computed sequence of simple eigenvalues and eigenfunctions. This justifies the use of the proven saturation property for a class of reliable and efficient hierarchical a posteriori error estimators. Numerical experiments confirm that the saturation property is present even for very coarse meshes for many examples; in other cases the smallness assumption on the initial mesh may be severe.

• 出版日期2014-12