# Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations

William Layton; Nathaniel Mays; Monika Neda; Catalin Trenchea

- Volume: 48, Issue: 3, page 765-793
- ISSN: 0764-583X

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topLayton, William, et al. "Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.3 (2014): 765-793. <http://eudml.org/doc/273111>.

@article{Layton2014,

abstract = {We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing BDF2 time discretization in Step 1.1, and (ii) more general (linear or nonlinear) regularization operators in Step 1.1. We give a complete stability analysis, derive conditions on the Step 1.1 regularization operator for which the combination has good stabilization effects, characterize the numerical dissipation induced by Step 1.1, prove an asymptotic error estimate incorporating the numerical error of the method used in Step 1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.},

author = {Layton, William, Mays, Nathaniel, Neda, Monika, Trenchea, Catalin},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {modular regularization; BDF2 time discretization; Navier-Stokes equations; turbulence; finite element method},

language = {eng},

number = {3},

pages = {765-793},

publisher = {EDP-Sciences},

title = {Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations},

url = {http://eudml.org/doc/273111},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Layton, William

AU - Mays, Nathaniel

AU - Neda, Monika

AU - Trenchea, Catalin

TI - Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 3

SP - 765

EP - 793

AB - We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing BDF2 time discretization in Step 1.1, and (ii) more general (linear or nonlinear) regularization operators in Step 1.1. We give a complete stability analysis, derive conditions on the Step 1.1 regularization operator for which the combination has good stabilization effects, characterize the numerical dissipation induced by Step 1.1, prove an asymptotic error estimate incorporating the numerical error of the method used in Step 1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.

LA - eng

KW - modular regularization; BDF2 time discretization; Navier-Stokes equations; turbulence; finite element method

UR - http://eudml.org/doc/273111

ER -

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