Ariel L. Lombardi

Error estimates on anisotropic ₁ elements for functions in weighted Sobolev spaces

In this paper we prove error estimates for a piecewise Q 1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained.

Continuity of Optimal Values and Solutions for Control of Markov Chains with Constraints

We consider in this paper constrained Markov decision processes. This type of control model has many applications in telecommunications and other fields [E. Altman and A. Shwartz, IEEE Trans. Automat. Control, 34 (1989), pp. 1089--1102, E. A. Feinberg and M. I. Reiman, Probab. Engrg. Inform. Sci., 8 (1994), pp. 463--489, A. Hordijk and F. Spieksma, Adv. in Appl. Probab., 21 (1989), pp. 409--431, A. Lazar, IEEE Trans. Automat. Control, 28 (1983), pp. 1001--1007, P. Nain and K. W. Ross, IEEE Trans. Automat. Control, 31 (1986), pp. 883--888, K. W. Ross and B. Chen, IEEE Trans. Automat. Control, 33 (1988), pp. 261--267]. We address the issue of the convergence of the value and optimal policies of the problem with discounted costs, to the ones for the problem with expected average cost. We consider the general multichain ergodic structure. We present two stability results in this paper. We establish the continuity of optimal values and solutions of as well as some type of robustness of some suboptimal solutions in the discount factor. Our proof relies on same general theory on continuity of values and solutions in convex optimization that relies on well-known notions of

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

\Gamma

Anisotropic error estimates for an interpolant defined via moments

-convergence.

Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra

AbstractSimilarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type

Error Estimates for the Raviart-Thomas Interpolation Under the Maximum Angle Condition

- q_0 t^{ - (1/2)}

A BLOCK SOLVER FOR THE EXPONENTIALLY FITTED IIPG-0 METHOD

is imposed on the fixed face x = 0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q0 is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x = 0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo