INVESTIGADORES
DARI Enzo Alberto
artículos
Título:
A posteriori error estimates for non-conforming approximation of eigenvalue problems
Autor/es:
ENZO A. DARI; RICARDO G. DURÁN; CLAUDIO PADRA
Revista:
APPLIED NUMERICAL MATHEMATICS
Editorial:
ELSEVIER SCIENCE BV
Referencias:
Lugar: Amsterdam; Año: 2012 vol. 62 p. 580 - 591
ISSN:
0168-9274
Resumen:
We consider the approximation of eigenvalue problem for
the Laplacian by the CrouzeixRaviart non-conforming finite elements in
two and three dimensions.
Extending known techniques
for source problems, we introduce a posteriori error estimators for
eigenvectors and eigenvalues. We prove that the error estimator is
equivalent to the energy norm of the eigenvector error up to higher
order terms. Moreover, we prove that our estimator provides an upper
bound for the error in the approximation of the first eigenvalue, also
up to higher order terms.
We present numerical
examples of an adaptive procedure based on our error estimator in two
and three dimensions. These examples show that the error in the adaptive
procedure is optimal in terms of the number of degrees of freedom.