Regions of Stability, Equivalence Theorems and the Courant-Friedrichs-Lewy Condition.
Relaxation models of phase transition flows
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
Resolvent estimates in for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes.
Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces.
Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
Roe Scheme for Two-layer Shallow Water Equations: Application to the Strait of Gibraltar
The flow trough the Strait of Gibraltar could be analyzed as a problem of two-layer hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The shallow water equations in both layers coupled together are an important tool to simulate this phenomenon. In this paper we perform an upwind schemes for hyperbolic equations based on the Roe approximate Riemann solver, to study the resulting model. The main goal assigned was to predict the location of the interface between the two layers....
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Runge-Kutta methods for parabolic equations with nonsmooth initial data
Schéma des différences finies pour un système d'équations paraboliques non linéaires avec dérivées mixtes
Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)
We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation...
Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions
Semi-discrétisation en temps pour les équations d'évolution paraboliques lorsque l'opérateur dépend du temps
Solution of contaminant transport with adsorption in porous media by the method of characteristics
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Solution of contaminant transport with adsorption in porous media by the method of characteristics
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard’s equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of porous medium type systems by linear approximation schemes.
Solution of Stefan problems by fully discrete linear schemes.
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I