A parallel stabilized quadratic equal-order finite element algorithm for the steady Navier–Stokes equations

Abstract

This paper is concerned with a parallel stabilized quadratic equal-order finite element algorithm for the steady incompressible Navier–Stokes equations where a fully overlapping domain decomposition is used for parallelization. The basic idea of the studied algorithm is that each processor independently calculates a local stabilized solution in an interesting subdomain on a multiscale mesh that is fine around the subdomain and coarse on the rest of subdomain. The present algorithm can be solved simultaneously by the existing Navier–Stokes codes without substantial recoding. In the light of local a priori estimate for stabilized finite element solution, we analyse the error bound of the stabilized solution. Moreover, several parallel iterative stabilized quadratic equal-order finite element algorithms are presented, and three numerical examples which confirm the high efficiency of the parallel stabilized algorithms are provided.

Keywords:

• Navier–Stokes equations
• stabilized quadratic equal-order method
• finite element
• parallel algorithm
• domain decomposition

AMS SUBJECT CLASSIFICATIONS:

• 76D05
• 35Q30
• 65N55
• 65N30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation of China [grant number 11361016], and the Natural Science Foundation of Chongqing Municipality, China [grant number cstc2021jcyj-msxmX1044].