KRELL , Stella

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We study the approximation of solutions to the stationary Stokes problem with a piecewise constant viscosity coefficient (interface Stokes problem) in the discrete duality finite volume (DDFV) framework. In order to take into account the discontinuities and to prevent consistency defect in the scheme, we propose to modify the definition of the...

We develop a Discrete Duality Finite Volume (\DDFV{}) method for the three-dimensional steady Stokes problem with a variable viscosity coefficient on polyhedral meshes. Under very general assumptions on the mesh, which may admit non-convex and non-conforming polyhedrons, we prove the stability and well-posedness of the scheme. We also prove the...

We made a comparison between a Discrete Duality Finite Volume (DDFV) scheme and a Hybrid Finite Volume (HFV) scheme for a drift-diffusion model with mixed boundary conditions on general meshes. Both schemes are based on a nonlinear discretisation of the convection-diffusion fluxes, which ensures the positivity of the discrete densities. We...

We made a comparison between a Discrete Duality Finite Volume (DDFV) scheme and a Hybrid Finite Volume (HFV) scheme for a drift-diffusion model with mixed boundary conditions on general meshes. Both schemes are based on a nonlinear discretisation of the convection-diffusion fluxes, which ensures the positivity of the discrete densities. We...

We introduce a nonlinear DDFV scheme for an anisotropic linear convection-diffusion equationwith mixed boundary conditions and we establish the exponential decay of the scheme towards its steady-state.

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier--Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and is (relatively) inexpensive thanks to the possibility of statically condensing a subset of the unknowns at...

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We consider the homogenization of a coupled system of PDEs describing flows in highly heterogeneous porous media. Due to the coupling, the effective coefficients always depend on the slow variable, even in the simple case when the porosity is taken purely periodic. Therefore the most important part of the computational time for the numerical...

Over the last five years, classical and optimized Schwarz methods have been developed for anisotropic elliptic problems discretized with Discrete Duality Finite Volume (DDFV) schemes. Like for Discontinuous Galerkin methods (DG), it is not a priori clear how to appropriately discretize transmission conditions with DDFV, and numerical...

We consider DDFV discretization of the Navier-Stokes equations where the convection fluxes are computed by means of B-schemes, generalizing the classical centered and upwind discretizations. This study is motivated by the analysis of domain decomposition approaches. We investigate on numerical grounds the convergence of the method.

We propose and analyze non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier-Stokes problem with Discrete Duality Finite Volume discretizations. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method and...

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We propose a Discrete Duality Finite Volume scheme (DDFV for short) for the unsteady incom-pressible Navier-Stokes problem with outflow boundary conditions. As in the continuous case, those conditions are derived from a weak formulation of the equations and they provide an energy estimate of the solution. We prove wellposedness of the scheme...

''Discrete Duality Finite Volume'' schemes (DDFV for short) on general 2D meshes, in particular non conforming ones, are studied for the Stokes problem with Dirichlet boundary conditions. The DDFV method belongs to the class of staggered schemes since the components of the velocity and the pressure are approximated on different meshes. In this...

The aim of this work is to analyze " Discrete Duality Finite Volume " schemes (DDFV for short) on general meshes by adapting the theory known for the linear Stokes problem with Dirichlet boundary conditions to the case of Neu-mann boundary conditions on a fraction of the boundary. We prove well-posedness for stabilized schemes and we derive...

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We propose and analyze non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier–Stokes problem with Discrete Duality Finite Volume (DDFV) discretization. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method...

The Poisson-Nernst Planck (PNP) system of equations is widely recognized as the standard model for characterizing the electrodiffusion of ions in electrolytes, including ionic dynamics in the cellular cytosol. This non-linear system presents challenges for both modeling and simulations, due to the presence of a stiff boundary layer tightly...

''Discrete Duality Finite Volume'' schemes (DDFV for short) on general 2D meshes, in particular non conforming ones, are studied for the Stokes problem with Dirichlet boundary conditions. The DDFV method belongs to the class of staggered schemes since the components of the velocity and the pressure are approximated on different meshes. In this...

In this paper, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration....

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation relation. This relation is of paramount importance to capture the long-time behavior of the problem in an...

In this paper, we are interested in the finite volume approximation of a system describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion...

We introduce a nonlinear DDFV scheme for a convection-diffusion equation. The scheme conserves the mass, satisfies an energy-dissipation inequality and provides positive approximate solutions even on very general grids. Numerical experiments illustrate these properties.