A posteriori error estimates for the Steklov eigenvalue problem

Authors:
María G. Armentano;Claudio Padra
Affiliations:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina;Centro Atómico Bariloche, 4800 Bariloche, Argentina
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 6
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Abstract

In this paper we introduce and analyze an a posteriori error estimator for the linear finite element approximations of the Steklov eigenvalue problem. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, up to higher order terms, the estimator is equivalent to the energy norm of the error. Finally, we prove that the volumetric part of the residual term is dominated by a constant times the edge residuals, again up to higher order terms.