María G. Armentano

Error estimates for moving least square approximations

Abstract In this paper we obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives. We prove that, under appropriate hypothesis on the weight function and the distribution of points, the method produces optimal order approximations of the function and its first and second derivatives. As a consequence, we obtain optimal order error estimates for Galerkin approximations of coercive problems. Finally, as an application of the moving least square method we consider a convection–diffusion equation and propose a way of introducing up-wind by means of a non-symmetric weight function. We present several numerical results showing the good behavior of the method.

A Posteriori Error Estimates of stabilized Low-Order Mixed Finite Elements for the Stokes Eigenvalue Problem

In this paper we obtain a priori and a posteriori error estimates for stabilized low-order mixed finite element methods for the Stokes eigenvalue problem. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. 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. We also present some numerical tests which show the performance of the adaptive scheme.

Finite element approximations in a non-Lipschitz domain: Part II

Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matematica; Argentina