## A mixed finite element method for nearly incompressible multiple-network poroelasticity.(English)Zbl 1417.65162

Excerpt from the abstract of the manuscript: “The authors present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. Here, the authors focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, they propose a new mixed finite element formulation based on introducing an additional total pressure variable. By presenting energy estimates for the continuous solutions and a priori error estimates for a family of compatible semidiscretizations, they show that this formulation is robust for nearly incompressible materials, small storage coefficients, and small or vanishing transfer between networks. These theoretical results are corroborated by numerical experiments, including results for blood and interstitial fluid flow interactions.”

### MSC:

 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 92C10 Biomechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74L15 Biomechanical solid mechanics 92C35 Physiological flow 35Q92 PDEs in connection with biology, chemistry and other natural sciences

### Software:

poroelasticity; FEniCS
Full Text:

### References:

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