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Second‐order Galerkin‐Lagrange method for the Navier‐Stokes equations (retracted article)
Author(s) -
Bensaada Mohamed,
Esselaoui Driss,
Saramito Pierre
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20080
Subject(s) - mathematics , galerkin method , partial derivative , partial differential equation , lagrange multiplier , navier–stokes equations , convergence (economics) , nonlinear system , stability (learning theory) , order (exchange) , mathematical analysis , computer science , mathematical optimization , physics , finance , quantum mechanics , machine learning , compressibility , economics , thermodynamics , economic growth
The Lagrange-Galerkin method, has been proposed for the numerical treatment of convectiondominated diffusion equation (see [1–4]). It is based on combining a Galerkin finite element procedure with a special discretization of the material derivative along trajectories and has been shown to possess remarkable stability properties. Pironneau [5–8] have studied a characteristic finite element method for the Navier-Stokes equations. Other authors have used this method for the study and the simulation of viscoelastic fluid flows (see [9, 10]). In those works the first order characteristic finite element method is analyzed and used successfully. As for higher order methods, Pironneau et al. [8, 11] have mentioned a second-order Runge-Kutta (RK) approximation to the material derivative term, but they did not give a correct second-order approximation to the diffusion term. Hence, the final scheme is not of second order in time increment. For the convection-diffusion problems, Rui and Tabata [12] use also the second-order RK approximation to the material derivative term and point out that the scheme is second order in time increment.