Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem. Issue 6 (17th August 2021)

• Record Type: Journal Article
• Authors: Guo, Liming; Chen, Wenbin
• Other Names: Bochev Pavel guestEditor.; D'Elia Marta guestEditor.; Du Qiang guestEditor.; Hou Steve guestEditor.; Webster Clayton guestEditor.; Zhang Guannan guestEditor.
• Is Part Of: Numerical methods for partial differential equations. Volume 38:Issue 6(2022)
• Page Start: 1684
• Page End: 1712
• Publication Date: 2021-08-17
• Subjects: error estimates -- modified characteristic finite element method -- Navier–Stokes/Biot problem -- stability; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22830
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this article, a decoupled modified characteristic finite element method is proposed for the time‐dependent Navier–Stokes/Biot problem. In the numerical scheme, the implicit backward Euler scheme is used for the time discretization, whereas the coupling terms are treated explicitly. At each time step, we only need to solve two decoupled problems, one is the Navier–Stokes equations solved by the modified characteristic finite element method, and the other is Biot equations. The stability and the error estimates are established for the proposed fully discrete scheme. Numerical experiments are provided to illustrate the theory.