A mixed element analysis of the Biot's model with Darcy–Forchheimer flow. Issue 1 (12th August 2022)

• Record Type: Journal Article
• Authors: Li, Hongpeng; Rui, Hongxing
• Is Part Of: Numerical methods for partial differential equations. Volume 39:Issue 1(2023)
• Page Start: 577
• Page End: 599
• Publication Date: 2022-08-12
• Subjects: Darcy–Forchheimer law -- mixed finite element -- numerical experiments -- poroelasticity; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22904
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this article, we consider the three‐field Biot's consolidation model, in which the flow's velocity is described by Darcy–Forchheimer law. The model is nonlinear and the unknown variables are the displacement of the solid phase, fluid flux, and pore pressure. The linear finite element is proposed to approximate the solid displacement and the RT mixed finite element is proposed to approximate the fluid flux and pore pressure. The error estimates is given for semidiscrete scheme and fully discrete scheme. When analyzing the fully discrete scheme, no time step restriction is needed. Numerical tests for this method confirm the accuracy of the P1‐RT0‐P0 method when the constraint storage coefficient c 0 $$ {c}_0 $$ is positive and c 0 $$ {c}_0 $$ is null.