| Autor: |
Droniou, Jerome, Eymard, Robert |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Numer. Math. 132 (4), pp. 721-766, 2016 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00211-015-0733-6 |
| Popis: |
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite Volume methods. We show here that this framework can be applied to a family of degenerate non-linear parabolic equations (which contain in particular the Richards', Stefan's and Leray--Lions' models), and we prove a uniform-in-time strong-in-space convergence result for the gradient scheme approximations of these equations. In order to establish this convergence, we develop several discrete compactness tools for numerical approximations of parabolic models, including a discontinuous Ascoli-Arzel\`a theorem and a uniform-in-time weak-in-space discrete Aubin-Simon theorem. The model's degeneracies, which occur both in the time and space derivatives, also requires us to develop a discrete compensated compactness result. |
| Databáze: |
arXiv |
| Externí odkaz: |
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