# A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 1, page 141-174
- ISSN: 0764-583X

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topAbboud, Hyam, and Sayah, Toni. "A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme." ESAIM: Mathematical Modelling and Numerical Analysis 42.1 (2008): 141-174. <http://eudml.org/doc/250283>.

@article{Abboud2008,

abstract = {
We study a two-grid scheme fully discrete in time and
space for solving the Navier-Stokes system. In the first step, the
fully non-linear problem is discretized in space on a coarse grid
with mesh-size H and time step k. In the second step, the
problem is discretized in space on a fine grid with mesh-size h
and the same time step, and linearized around the velocity uH
computed in the first step. The two-grid strategy is motivated by
the fact that under suitable assumptions, the contribution of
uH to the error in the non-linear term, is measured in the
L2 norm in space and time, and thus has a higher-order than if
it were measured in the H1 norm in space. We present the
following results: if h = H2 = k, then the global error of
the two-grid algorithm is of the order of h, the same as would
have been obtained if the non-linear problem had been solved
directly on the
fine grid.
},

author = {Abboud, Hyam, Sayah, Toni},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Two-grid scheme; non-linear problem;
incompressible flow; time and space discretizations; duality
argument; “superconvergence”.; global error estimate; coarse grid; fine grid},

language = {eng},

month = {1},

number = {1},

pages = {141-174},

publisher = {EDP Sciences},

title = {A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme},

url = {http://eudml.org/doc/250283},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Abboud, Hyam

AU - Sayah, Toni

TI - A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/1//

PB - EDP Sciences

VL - 42

IS - 1

SP - 141

EP - 174

AB -
We study a two-grid scheme fully discrete in time and
space for solving the Navier-Stokes system. In the first step, the
fully non-linear problem is discretized in space on a coarse grid
with mesh-size H and time step k. In the second step, the
problem is discretized in space on a fine grid with mesh-size h
and the same time step, and linearized around the velocity uH
computed in the first step. The two-grid strategy is motivated by
the fact that under suitable assumptions, the contribution of
uH to the error in the non-linear term, is measured in the
L2 norm in space and time, and thus has a higher-order than if
it were measured in the H1 norm in space. We present the
following results: if h = H2 = k, then the global error of
the two-grid algorithm is of the order of h, the same as would
have been obtained if the non-linear problem had been solved
directly on the
fine grid.

LA - eng

KW - Two-grid scheme; non-linear problem;
incompressible flow; time and space discretizations; duality
argument; “superconvergence”.; global error estimate; coarse grid; fine grid

UR - http://eudml.org/doc/250283

ER -

## References

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