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Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

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

We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by a posteriori estimates of...

Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by a posteriori estimates of...

Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by a posteriori estimates of...

Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.

Sylvie Benzoni-Gavage, Denis Serre (1994)

Revista Matemática Iberoamericana

We are concerned with a strictly hyperbolic system of conservation laws ut + f(u)x = 0, where u runs in a region Ω of Rp, such that two of the characteristic fields are genuinely non-linear whereas the other ones are of Blake Temple's type. We begin with the case p = 3 and show, under more or less technical assumptions, that the approximate solutions (uε)ε>0 given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as ε goes to 0. The first...

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