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Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

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

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...

Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...

Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...

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...

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