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The main goal of this paper is to propose a convergent finite volume method for a reaction–diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes a ...
In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection betwe ...
An epidemic model is formulated by a reaction–diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the ...
A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined w ...
An adaptive multiresolution scheme is proposed for the numerical solution of a spatially two-dimensional model of sedimentation of suspensions of small solid particles dispersed in a viscous fluid. This model consists in a version of the Stokes equations f ...
The bidomain model of electrical activity of myocardial tissue consists of a possibly degenerate parabolic PDE coupled with an elliptic PDE for the transmembrane and extracellular potentials, respectively. This system of two scalar PDEs is supplemented by ...
We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate dif ...
A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid desc ...
We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, ...
We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membra ...