Superconvergent Finite Element Postprocessing for Eigenvalue Problems with Nonlocal Boundary Conditions

Authors:
A. B. Andreev;M. R. Racheva
Affiliations:
Department of Informatics, Technical University of Gabrovo, Gabrovo, Bulgaria 5300;Department of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria 5300
Venue:
Large-Scale Scientific Computing
Year:
2009

Citing 3
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Abstract

We present a postprocessing technique applied to a class of eigenvalue problems on a convex polygonal domain 茂戮驴in the plane, with nonlocal Dirichlet or Neumann boundary conditions on $\Gamma_1 \subset \partial \Omega$. Such kind of problems arise for example from magnetic field computations in electric machines. The postprocessing strategy accelerates the convergence rate for the approximate eigenpair. By introducing suitable finite element space as well as solving a simple additional problem, we obtain good approximations on a coarse mesh. Numerical results illustrate the efficiency of the proposed method.