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Mathematical study of a petroleum-engineering scheme

Robert Eymard, Raphaèle Herbin, Anthony Michel (2003)

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

Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...

Mathematical study of a petroleum-engineering scheme

Robert Eymard, Raphaèle Herbin, Anthony Michel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...

Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations

Nikolai Yu. Bakaev, Michel Crouzeix, Vidar Thomée (2006)

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

In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions,...

Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations

Nikolai Yu. Bakaev, Michel Crouzeix, Vidar Thomée (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under...

Mixed finite element approximation for a coupled petroleum reservoir model

Mohamed Amara, Daniela Capatina-Papaghiuc, Bertrand Denel, Peppino Terpolilli (2005)

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

In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....

Mixed finite element approximation for a coupled petroleum reservoir model

Mohamed Amara, Daniela Capatina-Papaghiuc, Bertrand Denel, Peppino Terpolilli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....

Mixed methods for the approximation of liquid crystal flows

Chun Liu, Noel J. Walkington (2002)

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

The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H 2 ( Ω ) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.

Mixed Methods for the Approximation of Liquid Crystal Flows

Chun Liu, Noel J. Walkington (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H2(Ω) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.

Model analysis of BPX preconditioner based on smoothed aggregation

Pavla Fraňková, Jan Mandel, Petr Vaněk (2015)

Applications of Mathematics

We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Shixin Xu, Minxin Chen, Sheereen Majd, Xingye Yue, Chun Liu (2014)

Molecular Based Mathematical Biology

Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical...

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