On the Postprocessing Technique for Eigenvalue Problems

Authors:
Andrey B. Andreev;Milena R. Racheva
Affiliations:
-;-
Venue:
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Year:
2002

Citing 1
Cited 2

Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems

Superconvergent Finite Element Postprocessing for Eigenvalue Problems with Nonlocal Boundary Conditions

Large-Scale Scientific Computing
Acceleration of convergence for eigenpairs approximated by means of non-conforming finite element methods

LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing

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Abstract

We present a new strategy of accelerating the convergence rate for the finite element solutions of the large class of linear eigenvalue problems of order 2m. The proposed algorithms have the superconvergence properties of the eigenvalues, as well as of the eigenfunctions. This improvement is obtained at a small computational cost. Solving a more simple additional problem, we get good finite element approximations on the coarse mesh. Different ways for calculating the postprocessed eigenfunctions are considered. The case where the spectral parameter appears linearly in the boundary conditions is discussed. The numerical examples, presented here, confirm the theoretical results and show the efficiency of the postprocessing method.