Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier–Stokes Equations

• Published in: Journal of scientific computing Vol. 89; no. 1; p. 8
• Main Authors: Han, Weimin, Czuprynski, Kenneth, Jing, Feifei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2021; Springer Nature B.V
• Subjects: Algorithms; Banach spaces; Boundary conditions; Computational Mathematics and Numerical Analysis; Error analysis; Finite element analysis; Finite element method; Flow velocity; Fluid flow; Incompressibility; Incompressible flow; Incompressible fluids; Inequality; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Theoretical; Navier–Stokes equations; Hemivariational inequality; Mixed finite element method; 47J20; Error estimation; Uniqueness; 76D05; Existence; 65N30
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-021-01614-9

In this paper, we develop and study the mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations (NS hemivariational inequality). The NS hemivariational inequality models the motion of a viscous incompressible fluid in a bounded domain, subject to a nonsmooth and nonconvex slip boundary condition. The incompressibility contraint is treated through a mixed formulation. Solution existence and uniqueness are explored. The mixed finite element method is applied to solve the NS hemivariational inequality and error estimates are derived. Numerical results are reported on the use of the P1b/P1 pair, illustrating the optimal convergence order predicted by the error analysis.