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Volume 8, Issue 4
A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data

Deepjyoti Goswami & Pedro D. Damázio

DOI: 10.4208/nmtma.2015.m1414

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 549-581.

Published online: 2015-08

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  • Abstract

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 $H^1$-norm and for pressure in $L^2$-norm. The analysis mainly focuses on the loss of regularity of the solution at $t = 0$ of the Navier-Stokes equations.

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@Article{NMTMA-8-549, author = {Deepjyoti Goswami and Pedro D. Damázio}, title = {A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {4}, pages = {549--581}, abstract = {

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 $H^1$-norm and for pressure in $L^2$-norm. The analysis mainly focuses on the loss of regularity of the solution at $t = 0$ of the Navier-Stokes equations.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1414}, url = {http://global-sci.org/intro/article_detail/nmtma/12423.html} }
TY - JOUR T1 - A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data AU - Deepjyoti Goswami & Pedro D. Damázio JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 549 EP - 581 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.m1414 UR - https://global-sci.org/intro/article_detail/nmtma/12423.html KW - AB -

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 $H^1$-norm and for pressure in $L^2$-norm. The analysis mainly focuses on the loss of regularity of the solution at $t = 0$ of the Navier-Stokes equations.

Deepjyoti Goswami and Pedro D. Damázio. (2015). A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data. Numerical Mathematics: Theory, Methods and Applications. 8 (4). 549-581. doi:10.4208/nmtma.2015.m1414
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