Claudio Baiocchi

Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)

Abstract The equivalence between stabilized finite element methods (or Galerkin-least-squares tyoe methods, Ga.l.s.) and the standard Galerkin method with bubble functions is established in an abstract framework. The results are applicable to various finite element spaces, including high order elements, and applications to the advective diffusive model and to the Stokes problem are presented, illustrating the potential of the abstract theory introduced here.

A filtration problem in a porous medium with variable permeability

SuntoUn problema di frontiera libera (moto di un fluido attraverso una diga in terra non omogenea) è ricondotto allo studio di una disequazione variazionale. Si danno condizioni sul coefficiente di permeabilità sufficienti ad assicurare che la parte bagnata della diga è un sottografico.

Stabilization of Galerkin Methods and Applications to Domain Decomposition

We present an abstract stabilization method which covers previous concrete applications to advection-diffusion equations and to the Stokes equations for incompressible fluids. We then apply the method to stabilize domain decomposition formulations for elliptic problems. We obtain a method that allows the treatment of internal variables, interface variables and Lagrange multipliers (normal derivatives) by piecewise polynomials of arbitrary order.

Optimal error estimates for linear parabolic problems under minimal regularity assumptions

We study the approximation of linear parabolic problems by means of Galerkin approximation in space and θ-method in time. The error is evaluated in norms of typeHtδ (H1x) ⋂Htδ+1/2 (Lx2) for |δ|≤1/2. We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.

On the equivalence of A-stability and G-stability

Abstract We prove an algebraic result which gives a new characterization of the A-stability property for linear multistep methods. This enables us to obtain a new simple proof of the equivalence between A-stability and G-stability for one-leg methods. Using the algebraic result, we also give an alternative proof of the second Dahlquist barrier.

Uniqueness for two immiscible fluids in a one-dimensional porous medium

In a recent paper [3] Evans and Friedman proved the existence of a global classical solution for two immiscibIe fluids in a one-dimensional porous medium; a solution in a weaker sense was earlier established by Evans [l] [2]. As for uniqueness, the only known proof until now has been that due to Fulks and Guenther [.5] (who also proved local existence). This proof relies upon integral equations representation of the problem and it has two drawbacks: (i) it requires more regularity assumptions on the data than are needed for the existence of a classical solution, and (ii) it is technically very lengthy and quite tedious. The main purpose of this paper is to give a simple and direct proof of uniqueness under precisely those regularity assumptions on the data which are needed for the existence of a global classical solution. Our approach is based on mapping the free boundary into a fixed line segment (see Schaeffer [6]). This approach can

Problemi Misti per L’Equazione del Galore

SuntoSi studia un’equazione differenziale astratta con dominio variabile. I risultati si applicano in particolare al problema misto, di tipo Cauchymisto, per l’equazione del calore (cfr. le successive (1.1), (1.2), (1.3), (1.4)) relativamente al quale,senza alcuna ipotesi di regolarità sull’ insieme portante il dato di Dirichlet, si dà un teorema di esistenza e unicità, in classi funzionali molto ampie per la soluzione e per i dati.RésuméOn étudie une équation différentielle abstraite à domaine variable. Les résultats s’appliquent en particulier au problème mixte, du type Cauchy-mÊlé, pour l’équation de la chaleur (cf. le problème 1.1) pour lequel,saris aucune hypothèse de regularité sur l’ensemble portant la donnée de Dirichlet, on donne un. théorème d’existence et unicité.

A mathematical model for transient analysis of computer systems

Abstract The study of computer system dynamic behavior is a prerequisite for the design and implementation of automatic mechanisms for performance control. An analytic technique for modelling the transient behavior of computer systems is presented and a suitable method for modelling job dynamics is given. The system model is discussed from the viewpoint of transient analysis with particular reference to bottleneck identification and to bottleneck migration analysis. A mathematical study is given together with a numerical algorithm. The model is validated on the basis of suitable experimental results.