Hybridized discontinuous Galerkin/hybrid mixed methods for a multiple network poroelasticity model with application in biomechanics. (English) Zbl 07779188
Summary: The quasi-static multiple-network poroelastic theory (MPET) model, first introduced in the context of geomechanics [G. Barenblatt, G. Zheltov, and I. Kochina, J. Appl. Math. Mech., 24 (1960), pp. 1286-1303], has recently found new applications in biomechanics. In practice, the parameters in the MPET equations can vary over several orders of magnitude which makes their stable discretization and fast solution a challenging task. Here, a new efficient parameter-robust hybridized discontinuous Galerkin method, which also features fluid mass conservation, is proposed for the MPET model. Its stability analysis, crucial for the well-posedness of the discrete problem, is performed, and cost-efficient parameter-robust preconditioners are derived. We present a series of numerical computations for a four-network MPET model of a human brain which demonstrate the performance of the new algorithms.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 76Z05 | Physiological flows |
| 74L15 | Biomechanical solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
fluid mass-conserving high-order discretization; parameter-robust LBB stability condition; norm-equivalent preconditioner; human brain modelingReferences:
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