A posteriori error estimates in finite element acoustic analysis

We present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies. We prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues. Numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement.Facultad de Ciencias Exacta

A posteriori error estimates in finite element acoustic analysis

We present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies. We prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues. Numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement.Facultad de Ciencias Exacta

Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods

This paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems. It is an extension to more general situations of known previous results about nonconforming methods. As an application of the present theory, convergence and optimal order error estimates are proved for the lowest order Crouzeix-Raviart approximation of the eigenpairs of two representative second-order elliptical operators.Facultad de Ciencias Exacta

Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods

This paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems. It is an extension to more general situations of known previous results about nonconforming methods. As an application of the present theory, convergence and optimal order error estimates are proved for the lowest order Crouzeix-Raviart approximation of the eigenpairs of two representative second-order elliptical operators.Facultad de Ciencias Exacta

Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods

This paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems. It is an extension to more general situations of known previous results about nonconforming methods. As an application of the present theory, convergence and optimal order error estimates are proved for the lowest order Crouzeix-Raviart approximation of the eigenpairs of two representative second-order elliptical operators.Facultad de Ciencias Exacta

Estimaciones a priori y a posteriori del error para problemas de autovalores

En este trabajo, se presenta una teoría de aproximación espectral para operadores lineales y acotados en espacios de Hilbert. La teoría es abstracta y fue desarrollada para estudiar las aproximaciones por métodos no standard de problemas de autovalores formulados variacionalmente.Facultad de Ciencias Exacta