## Displaying similar documents to “A mixed system of differential equations as a mathematical model of vibrations of continuum-discrete mechanical systems.”

### Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

ESAIM: Mathematical Modelling and Numerical Analysis

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In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones...

### Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

ESAIM: Mathematical Modelling and Numerical Analysis

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We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated a mixed finite element technique....

### An upwinding mixed finite element method for a mean field model of superconducting vortices

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.