poroelasticity swMATH ID: 39194 Software Authors: Lee, J. J.; Piersanti, E.; Mardal, K.-A.; Rognes, M. E. Description: A mixed finite element method for nearly incompressible multiple-network poroelasticity. In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium that is permeated by multiple fluid networks of differing characteristics. As such, the MPET equations represent a generalization of Biot’s equations, and numerical discretizations of the MPET equations face similar challenges. Here, we focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, we 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, we 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. Our primary interest in the MPET equations stems from the use of these equations in modeling interactions between biological fluids and tissues in physiological settings. So, we additionally present physiologically realistic numerical results for blood and interstitial fluid flow interactions. Homepage: https://zenodo.org/record/1215636#.YN2TLi35wRE Keywords: multiple-network poroelasticity; mixed finite element; incompressible; cerebral fluid flow Related Software: FEniCS; hypre; MUMPS; Firedrake; NGSolve; Netgen; PCPATCH; ALEA; deal.ii Cited in: 17 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A mixed finite element method for nearly incompressible multiple-network poroelasticity. Zbl 1417.65162Lee, J. J.; Piersanti, E.; Mardal, K.-A.; Rognes, M. E. 2019 all top 5 Cited by 39 Authors 6 Mardal, Kent-Andre 4 Kraus, Johannes K. 4 Lymbery, Maria 4 Rognes, Marie E. 4 Ruiz-Baier, Ricardo 3 Hong, Qingguo 3 Kuchta, Miroslav 2 Boon, Wietse M. 2 Kumar, Sarvesh 2 Lee, Jeonghun J. 2 Piersanti, Eleonora 2 Thompson, Travis B. 2 Verma, Nitesh 1 Altmann, Robert 1 Borregales Reverón, Manuel Antonio 1 Bürger, Raimund 1 De Oliveira Vilaca, Luis Miguel 1 Feng, Minfu 1 Gómez-Vargas, Bryan 1 Guo, Jun 1 Hornkjøl, Martin 1 Khan, Arbaz 1 Kumar, Kundan 1 Lederer, Philip Lukas 1 Maier, Roland 1 Mora, David 1 Nordbotten, Jan Martin 1 Oyarzúa, Ricardo 1 Philo, Fadi 1 Powell, Catherine Elizabeth 1 Qi, Wenya 1 Radu, Florin Adrian 1 Rhebergen, Sander 1 Schöberl, Joachim 1 Seshaiyer, Padmanabhan 1 Solano, Manuel E. 1 Wang, Junping 1 Wheeler, Mary Fanett 1 Zúñiga, Paulo all top 5 Cited in 12 Serials 5 SIAM Journal on Scientific Computing 2 Journal of Scientific Computing 1 Applicable Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 BIT 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Advances in Computational Mathematics 1 Computational Geosciences 1 Multiscale Modeling & Simulation 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Electronic Research Archive Cited in 5 Fields 17 Numerical analysis (65-XX) 13 Fluid mechanics (76-XX) 11 Partial differential equations (35-XX) 11 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) Citations by Year