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Finite volume schemes for fully non-linear elliptic equations in divergence form
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Finite volume schemes for fully non-linear elliptic equations in divergence form

Jerome Droniou

Abstract

finite volume schemes irregular grids non-linear elliptic equations Leray-Lions operators 65N12; 35J65; 65N30
We construct finite volume schemes, on unstructured and irregular grids, for non-linear elliptic equations of the p-Laplacian kind: -div(|Du|^{p-2}Du)=f. 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.
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