Low‐order stabilized finite element methods for the unsteady Stokes/Navier‐Stokes equations with friction boundary conditions. (24th January 2018)

• Record Type: Journal Article
• Authors: Qiu, Hailong; Xue, Changfeng; Xue, Liang
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 5(2018)
• Page Start: 2119
• Page End: 2139
• Publication Date: 2018-01-24
• Subjects: error estimates -- friction boundary conditions -- low‐order element -- stabilized method -- unsteady Stokes/Navier‐stokes equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4738
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider low‐order stabilized finite element methods for the unsteady Stokes/Navier‐Stokes equations with friction boundary conditions. The time discretization is based on the Euler implicit scheme, and the spatial discretization is based on the low‐order element ( P 1 − P 1 or P 1 − P 0 ) for the approximation of the velocity and pressure. Moreover, some error estimates for the numerical solution of fully discrete stabilized finite element scheme are obtained. Finally, numerical experiments are performed to confirm our theoretical results.