## Analysis of a sequential regularization method for the unsteady Navier-Stokes equations

Publication
, Journal Article

Lu, X; Lin, P; Liu, JG

Published in: Mathematics of Computation

July 1, 2008

The incompressibility constraint makes Navier-Stokes equations difficult. A reformulation to a better posed problem is needed before solving it numerically. The sequential regularization method (SRM) is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods. In the paper, we study the existence and uniqueness for the solution of the SRM and provide a simple proof of the convergence of the solution of the SRM to the solution of the Navier-Stokes equations. We also give error estimates for the time discretized SRM formulation. ©2008 American Mathematical Society.

### Duke Scholars

## Published In

Mathematics of Computation

## DOI

## ISSN

0025-5718

## Publication Date

July 1, 2008

## Volume

77

## Issue

263

## Start / End Page

1467 / 1494

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Lu, X., Lin, P., & Liu, J. G. (2008). Analysis of a sequential regularization method for the unsteady Navier-Stokes equations.

*Mathematics of Computation*,*77*(263), 1467–1494. https://doi.org/10.1090/S0025-5718-08-02087-5Lu, X., P. Lin, and J. G. Liu. “Analysis of a sequential regularization method for the unsteady Navier-Stokes equations.”

*Mathematics of Computation*77, no. 263 (July 1, 2008): 1467–94. https://doi.org/10.1090/S0025-5718-08-02087-5.Lu X, Lin P, Liu JG. Analysis of a sequential regularization method for the unsteady Navier-Stokes equations. Mathematics of Computation. 2008 Jul 1;77(263):1467–94.

Lu, X., et al. “Analysis of a sequential regularization method for the unsteady Navier-Stokes equations.”

*Mathematics of Computation*, vol. 77, no. 263, July 2008, pp. 1467–94.*Scopus*, doi:10.1090/S0025-5718-08-02087-5.Lu X, Lin P, Liu JG. Analysis of a sequential regularization method for the unsteady Navier-Stokes equations. Mathematics of Computation. 2008 Jul 1;77(263):1467–1494.

## Published In

Mathematics of Computation

## DOI

## ISSN

0025-5718

## Publication Date

July 1, 2008

## Volume

77

## Issue

263

## Start / End Page

1467 / 1494

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics