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Moving mesh for the axisymmetric harmonic map flow

Benoit Merlet, Morgan Pierre (2005)

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

We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the L 2 -gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularity at the...

Moving mesh for the axisymmetric harmonic map flow

Benoit Merlet, Morgan Pierre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the L2-gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularity at the...

Multicomponent flow in a porous medium. Adsorption and Soret effect phenomena : local study and upscaling process

Serge Blancher, René Creff, Gérard Gagneux, Bruno Lacabanne, François Montel, David Trujillo (2001)

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

Our aim here is to study the thermal diffusion phenomenon in a forced convective flow. A system of nonlinear parabolic equations governs the evolution of the mass fractions in multicomponent mixtures. Some existence and uniqueness results are given under suitable conditions on state functions. Then, we present a numerical scheme based on a “mixed finite element” method adapted to a finite volume scheme, of which we give numerical analysis. In a last part, we apply an homogenization technique to...

Multicomponent flow in a porous medium. Adsorption and Soret effect phenomena: local study and upscaling process

Serge Blancher, René Creff, Gérard Gagneux, Bruno Lacabanne, François Montel, David Trujillo (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Our aim here is to study the thermal diffusion phenomenon in a forced convective flow. A system of nonlinear parabolic equations governs the evolution of the mass fractions in multicomponent mixtures. Some existence and uniqueness results are given under suitable conditions on state functions. Then, we present a numerical scheme based on a "mixed finite element"method adapted to a finite volume scheme, of which we give numerical analysis. In a last part, we apply an homogenization technique to...

Multilevel correction adaptive finite element method for semilinear elliptic equation

Qun Lin, Hehu Xie, Fei Xu (2015)

Applications of Mathematics

A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary...

Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem

Aihui Zhou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a multi-parameter error resolution technique is applied into a mixed finite element method for the Stokes problem. By using this technique and establishing a multi-parameter asymptotic error expansion for the mixed finite element method, an approximation of higher accuracy is obtained by multi-processor computers in parallel.

Currently displaying 1221 – 1240 of 2193