A stabilized difference finite element method for the 3D steady Stokes equations

Xiaoli Lu, Pengzhan Huang, Xinlong Feng and Yinnian He

Applied Mathematics and Computation, 2022, vol. 430, issue C

Abstract: A stabilized difference finite element (SDFE) method based on the finite element pair ((P1,P1,P1)×P1)×(P1×P0) is presented for the 3D steady Stokes equations. The difference finite element method consists of combining the finite difference discretization based on the P1×P0-element in the z-direction and the finite element discretization based on the (P1,P1,P1)×P1-element in the (x,y)-plane. In this way, the numerical solution of the 3D steady Stokes equations can be transmitted into a series of the finite element solution pair (whk,phk) of the 2D steady Stokes equations and the finite element solution u3hk of the elliptic equation. The core of the stabilized method is to characterize the Ladyzhenskaya-Babusˇka-Brezzi “deficiency” of the unstable finite element pair with an appropriate operator, and the application of the operator in the stabilized mixed variational equations. The rigorous stability analysis and error estimation are developed, showing that the SDFE method is stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions and verifying the accuracy of the considered method.

Keywords: Stabilized difference finite element method; 3D steady stokes equations; Finite element pair ((P1,P1,P1)×P1)×(P1×P0); Optimally convergent (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300322003447
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003447

DOI: 10.1016/j.amc.2022.127270

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().