Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations


Authors: Garth A. Baker, Vassilios A. Dougalis and Ohannes A. Karakashian
Journal: Math. Comp. 39 (1982), 339-375
MSC: Primary 65M60; Secondary 65N30, 76D05
MathSciNet review: 669634
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider approximating the solution of the initial and boundary value problem for the Navier-Stokes equations in bounded two- and three-dimensional domains using a nonstandard Galerkin (finite element) method for the space discretization and the third order accurate, three-step backward differentiation method (coupled with extrapolation for the nonlinear terms) for the time stepping. The resulting scheme requires the solution of one linear system per time step plus the solution of five linear systems for the computation of the required initial conditions; all these linear systems have the same matrix. The resulting approximations of the velocity are shown to have optimal rate of convergence in $ {L^2}$ under suitable restrictions on the discretization parameters of the problem and the size of the solution in an appropriate function space.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M60, 65N30, 76D05

Retrieve articles in all journals with MSC: 65M60, 65N30, 76D05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0669634-0
Article copyright: © Copyright 1982 American Mathematical Society