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arXiv · 1211.3342

A two-level finite element method for time-dependent incompressible Navier-Stokes equations with non-smooth initial data

Deepjyoti Goswami·Pedro D. Damázio
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Abstract

In this article, we analyze a two-level 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 $H^1$-norm and for pressure in $L^2$-norm. The analysis takes in to account the loss of regularity of the solution at $t=0$ of the Navier-Stokes equations.

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Deepjyoti Goswami, Pedro D. Damázio. 2012-11-14. A two-level finite element method for time-dependent incompressible Navier-Stokes equations with non-smooth initial data. https://doi.org/10.4208/nmtma.2015.m1414

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