The purpose of this paper is to propose a proof for the PoincaréFriedrichs inequality for piecewise H1 functions on anisotropic meshes. By verifying suitable assumptions involved in the newly proposed proof, we show that the Poincaré-Friedrichs inequality for piecewise H1 functions holds independently of the aspect ratio which characterizes the shape-regular condition in finite element analysis...

In this paper we develop and analyse a new a posteriori error estimator for general Friedrichs' systems valid for most classical nite element approximations. This error estimator is based on comparison between an appropriate norm of the exact error, and the L 2-norm of the residuals of the approximate solution. We prove that the estimator is independent of the dimension of the space and of the ...

We discuss a generalized Schrödinger operator in L2(Rd), d = 2, 3, with an attractive singular interaction supported by a (d−1)-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if d = 2, or surface waves in presence of a finite number of impurities if d = 3. We analyze the discrete spectrum, and furthermore,...

The Friedrichs extension and the Krein extension of a positive operator in a Krein space are characterized in terms of their spectral functions in a Krein space.

Staggered grid finite volume methods (also called central schemes) were introduced in one dimension by Nessyahu and Tadmor in 1990 in order to avoid the necessity of having information on solutions of Riemann problems for the evaluation of numerical fluxes. We consider the general case in multidimensions and on general staggered grids which have to satisfy only an overlap assumption. We interpr...