### Vanishing non-local regularization of a scalar conservation law.

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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the $p$-laplacian kind: $-div\left(\right|\nabla u{|}^{p-2}\nabla u)=f$ (with $1\<p\<\infty $). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -Laplacian kind: -div(|∇∇) = ƒ (with 1 < < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

We prove the convergence of a finite volume method for a noncoercive linear elliptic problem, with right-hand side in the dual space of the natural energy space of the problem.

In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity,...

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