EN FR
EN FR


Section: New Results

New results related to FreeFem++

In [10] , we propose an efficient algorithm for the numerical approximation of metrics, used for anisotropic mesh adaptation on triangular meshes with finite element computations. We derive the metrics from interpolation error estimates expressed in terms of higher order derivatives, for the P-k-Lagrange finite element, k>1. Numerical examples of mesh adaptation done using metrics computed with our Algorithm, and derived from higher order derivatives as error estimates, show that we obtain the right directions of anisotropy.

In [2] , we consider a system of two reaction-dispersion equations with non constant parameters. Both equations are coupled through the boundary conditions. We propose a mixed variational formulation that leads to a non symmetric saddle-point problem. We prove its well-posedness. Then, we develop a stabilized mixed finite element discretization of this problem and establish optimal a priori error estimates.

In [15] , we consider a model of soil water and nutrient transport with plant root uptake. The geometry of the plant root system is explicitly taken into account in the soil model. We first describe our modeling approach. Then, we introduce an adaptive mesh refinement procedure enabling us to accurately capture the geometry of the root system and small-scale phenomena in the rhizosphere. Finally, we present a domain decomposition technique for solving the problems arising from the soil model as well as some numerical results.