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Extension of a regularity result concerning the dam problem

Gianni Gilardi, Stephan Luckhaus (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.

Fefferman's SAK principle in one dimension

Frédéric Hérau (2000)

Annales de l'institut Fourier

In this article we give a complete proof in one dimension of an a priori inequality involving pseudo-differential operators: if a and b are symbols in S 1 , 0 2 such that | a | b , then for all ϵ > 0 we have the estimate a w u s 2 C ϵ ( b w u s 2 + u s + ϵ 2 ) for all u in the Schwartz space, where t is the usual H t norm. We use microlocalization of levels I, II and III in the spirit of Fefferman’s SAK principle.

Finite element approximation of a Stefan problem with degenerate Joule heating

John W. Barrett, Robert Nürnberg (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a fully practical finite element approximation of the following degenerate system t ρ ( u ) - . ( α ( u ) u ) σ ( u ) | φ | 2 , . ( σ ( u ) φ ) = 0 subject to an initial condition on the temperature, u , and boundary conditions on both u and the electric potential, φ . In the above ρ ( u ) is the enthalpy incorporating the latent heat of melting, α ( u ) > 0 is the temperature dependent heat conductivity, and σ ( u ) 0 is the electrical conductivity. The latter is zero in the frozen zone, u 0 , which gives rise to the degeneracy in this Stefan system. In addition to showing stability...

Finite element approximation of a Stefan problem with degenerate Joule heating

John W. Barrett, Robert Nürnberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a fully practical finite element approximation of the following degenerate system t ρ ( u ) - . ( α ( u ) u ) σ ( u ) | φ | 2 , . ( σ ( u ) φ ) = 0 subject to an initial condition on the temperature, u, and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0 is the electrical conductivity. The latter is zero in the frozen zone, u ≤ 0, which gives rise to the degeneracy in this Stefan...

Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities

Clément Cancès (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions. We approximate the solution of our problem thanks to a monotonous finite volume scheme. The convergence of the underlying discrete solution to a weak solution when the discretization step...

First order second moment analysis for stochastic interface problems based on low-rank approximation

Helmut Harbrecht, Jingzhi Li (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we propose a numerical method to solve stochastic elliptic interface problems with random interfaces. Shape calculus is first employed to derive the shape-Taylor expansion in the framework of the asymptotic perturbation approach. Given the mean field and the two-point correlation function of the random interface, we can thus quantify the mean field and the variance of the random solution in terms of certain orders of the perturbation amplitude by solving a deterministic elliptic interface...

Flaw identification in elastic solids: theory and experiments.

A. Gesualdo, F. Guarracino, V. Mallardo, V. Minutolo, L. Nunziante (1997)

Extracta Mathematicae

In this work the problem of identificating flaws or voids in elastic solids is addressed both from a theoretical and an experimental point of view. Following a so called inverse procedure, which is based on appropriately devised experiments and a particular bounding of the strain energy, a gap functional for flaw identification is proposed.

Currently displaying 581 – 600 of 1900