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The generalized finite volume SUSHI scheme for the discretization of the peaceman model

Mohamed Mandari; Mohamed Rhoudaf; Ouafa Soualhi — 2021

Applications of Mathematics

We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to 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 of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later,...

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul; Abdelkrim Barbara; Meryem El Lekhlifi; Mohamed Rhoudaf — 2012

Applicationes Mathematicae

We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $- d i v (a (x, u, \nabla u)) + g (x, u) = f - d i v F$ in Ω, where Ω is a bounded open domain of $ℝ^{N}$ , N ≥ 2 and $a : Ω \times ℝ \times ℝ^{N} \to ℝ^{N}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $\prod_{i = 1}^{N} L^{p^{'} (\cdot)} (Ω)$ .

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Currently displaying 1 – 7 of 7

The generalized finite volume SUSHI scheme for the discretization of the peaceman model

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

Leray Lions degenerated problem with general growth condition.

On the solvability of degenerated quasilinear elliptic problems.

Existence of solutions for nonlinear parabolic systems via weak convergence of truncations.

Existence result for variational degenerated parabolic problems via pseudo-monotonicity.

Higher order nonlinear degenerate elliptic problems with weak monotonicity.