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A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  10 November 2015

Deepjyoti Goswami and
Pedro D. Damázio
Deepjyoti Goswami*
Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam, Sonitpur, Assam -784028, India
Pedro D. Damázio
Affiliation:
Department of Mathematics, Universidade Federal do Paraná, Centro Politécnico, Curitiba, Cx.P: 19081, CEP: 81531-990, PR, Brazil
*
*Corresponding author

Abstract

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We analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

Keywords

Two-gridfinite elementNavier-Stokes equationsnon-smooth initial dataerror estimates

MSC classification

Secondary:65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65M12: Stability and convergence of numerical methods65M15: Error bounds

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 4 , November 2015, pp. 549 - 581
Copyright
Copyright © Global-Science Press 2015 

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