HIGH-ORDER MASS-LUMPED SCHEMES FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2020

HIGH-ORDER MASS-LUMPED SCHEMES FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

Résumé

We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we show are essentially necessary to obtain convergence and error estimates. Convergence is established without regularity assumption on the solution. A detailed analysis is then performed to understand the design properties that enable a scheme, despite these piecewise constant approximations and the degeneracy of the model, to satisfy high-order error estimates if the solution is piecewise smooth. Numerical tests, based on continuous and discontinuous approximation methods, are provided on a variety of 1D and 2D problems, showing the influence on the convergence rate of the nature of the degeneracy and of the design choices.
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Dates et versions

hal-02016807 , version 1 (12-02-2019)

Identifiants

  • HAL Id : hal-02016807 , version 1

Citer

Jerome Droniou, Robert Eymard. HIGH-ORDER MASS-LUMPED SCHEMES FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS. SIAM Journal on Numerical Analysis, 2020, 58 (1), pp.153-188. ⟨hal-02016807⟩
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