A posteriori error estimates for non-conforming approximation of

E. DARI; R. G. DURÁN; C. PADRA

APPLIED NUMERICAL MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2012 vol. 62 p. 580 - 591

0168-9274

 We consider the approximation of eigenvalue problem forthe laplacian by the Crouzeix-Raviart non conforming finite elements in two andthree dimensions. Extending known techniques for source problems, we introduce a posteriori errorestimators for eigenvectors and eigenvalues. We prove that the error estimatoris 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 theerror in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on ourerror estimator in two and three dimensions. These examples showthat the error in the adaptive procedure is optimal in terms ofthe number of degrees of freedom.