Raphaèle Herbin

3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids

We present a number of test cases and meshes that were designed as a benchmark for numerical schemes dedicated to the approximation of three-dimensional anisotropic and heterogeneous diffusion problems. These numerical schemes may be applied to general, possibly non conforming, meshes composed of tetrahedra, hexahedra and quite distorted general polyhedra. A number of methods were tested among which conforming finite element methods, discontinuous Galerkin finite element methods, cell-centered finite volume methods, discrete duality finite volume methods, mimetic finite difference methods, mixed finite element methods, and gradient schemes. We summarize the results presented by the participants to the benchmark, which range from the number of unknowns, the approximation errors of the solution and its gradient, to the minimum and maximum values and energy. We also compare the performance of several iterative or direct linear solvers for the resolution of the linear systems issued from the presented schemes.

Convergence of a finite volume scheme for nonlinear degenerate parabolic equations

Summary. One approximates the entropy weak solution u of a nonlinear parabolic degenerate equation

A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods

u_t+{\rm div}({\mathbf q} f(u))-\Delta \phi(u)=0

Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations

by a piecewise constant function

Lateral Diffusion of CO2 in Leaves Is Not Sufficient to Support Photosynthesis

u_{{\mathcal D}}

Finite volume approximation of elliptic problems and convergence of an approximate gradient

using a discretization

Existence of a solution to a coupled elliptic system

{\mathcal D}

A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case

in space and time and a finite volume scheme. The convergence of

Convergence Analysis of a Colocated Finite Volume Scheme for the Incompressible Navier-Stokes Equations on General 2D or 3D Meshes

u_{{\mathcal D}}

Convergence of finite volume schemes for semilinear convection diffusion equations

to u is shown as the size of the space and time steps tend to zero. In a first step, estimates on