@article{6ae6f8b9765441fb8c99d72550a7c3ec,
title = "Robust preconditioners for perturbed saddle-point problems and conservative discretizations of biot's equations utilizing total pressure",
abstract = "We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation of Biot's consolidation problem for linear poroelasticity (using displacement, filtration flux, total pressure, and fluid pressure). The stability of the continuous variational mixed problems, which hinges upon using adequately weighted spaces, is addressed in detail; and the efficacy of the proposed preconditioners, as well as their robustness with respect to relevant material properties, is demonstrated through several numerical experiments.",
keywords = "Equations of linear poroelasticity, Mixed finite element methods, Operator preconditioning, Perturbed saddle-point problems",
author = "Boon, \{Wietse M.\} and Miroslav Kuchta and Mardal, \{Kent Andre\} and Ricardo Ruiz-Baier",
note = "Funding Information: \textbackslash{}ast Submitted to the journal's Computational Methods in Science and Engineering section November 11, 2020; accepted for publication (in revised form) April 5, 2021; published electronically August 4, 2021. https://doi.org/10.1137/20M1379708 \textbackslash{}bfF \textbackslash{}bfu \textbackslash{}bfn \textbackslash{}bfd \textbackslash{}bfi \textbackslash{}bfn \textbackslash{}bfg : The first author's work was supported by the Dahlquist Research Fellowship, funded by Comsol AB. The second author's work was supported by the Research Council of Norway (NFR), grant 280709. The third author's work was supported by the Research Council of Norway, grants 300305 and 301013. The fourth author's work was supported by the Monash Mathematics Research Fund S05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers ``Digital biodesign and personalized healthcare{"}{"} 075-15-2020-926. Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
doi = "10.1137/20M1379708",
language = "English",
volume = "43",
pages = "B961--B983",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial \& Applied Mathematics (SIAM)",
number = "4",
}