A posteriori error estimation and adaptivity for multiple-network poroelasticity. (English) Zbl 07739201
Summary: The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled elliptic-parabolic problems, (ii) use this context to derive residual-based a posteriori error estimates and indicators for fully discrete MPET solutions and (iii) evaluate the performance of these error estimators in adaptive algorithms for a set of test cases: ranging from synthetic scenarios to physiologically realistic simulations of brain mechanics.
MSC:
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of 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 |
| 65Z05 | Applications to the sciences |
| 92-08 | Computational methods for problems pertaining to biology |
Keywords:
multiple network poroelasticity; a posteriori error estimates; adaptive finite element method; brain modelingReferences:
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