Hybridized Discontinuous Galerkin/Hybrid Mixed Methods for a Multiple Network Poroelasticity Model with Application in Biomechanics
Johannes Kraus, Philip L. Lederer, Maria Lymbery, Kevin Osthues, Joachim Schöberl · SIAM Journal on Scientific Computing · 2023
Abstract. 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.