Qingguo Hong,
Johannes Kraus
S. 202 - 226
doi:
10.1553/etna_vol48s202
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol48s202
Abstract:
This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (Darcy velocity), and pore pressure. Specific parameter-dependent norms provide the key in establishing the full parameter-robust inf-sup stability of the continuous problem. Therefore, the stability results presented here are uniform not only with respect to the Lamé parameter λ, but also with respect to all the other model parameters. This allows for the construction of a uniform block diagonal preconditioner within the framework of operator preconditioning. Stable discretizations that meet the required conditions for full robustness and guarantee mass conservation strongly, i.e., pointwise, are discussed and corresponding optimal error estimates proved.
Biot's consolidation model, three-field formulation, parameter-robust stability, conservative discretizations, uniform preconditioners, optimal error estimates
Published Online:
2018/06/19 13:36:21
Document Date:
2018/06/19 13:25:00
Object Identifier:
0xc1aa5576 0x003906c6
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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