Accurate Discretization Of Poroelasticity Without Darcy Stability -- Stokes-Biot Stability Revisited
| Autor: | Mardal, Kent-Andre, Rognes, Marie E., Thompson, Travis B. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10543-021-00849-0 |
| Popis: | In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability? Stokes-Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot's equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage coefficient and a vanishing hydraulic conductivity. The basic premise of a Stokes-Biot stable discretization is: one part Stokes stability and one part mixed Darcy stability. In this manuscript we remark on the observation that the latter condition can be generalized to a wider class of discrete spaces. In particular: a parameter-uniform inf-sup condition for a mixed Darcy sub-problem is not strictly necessary to retain the practical advantages currently enjoyed by the class of Stokes-Biot stable Euler-Galerkin discretization schemes. Comment: 26 pages |
| Databáze: | arXiv |
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