# A reduced basis element method for the steady Stokes problem

Alf Emil Løvgren; Yvon Maday; Einar M. Rønquist

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 3, page 529-552
- ISSN: 0764-583X

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topLøvgren, Alf Emil, Maday, Yvon, and Rønquist, Einar M.. "A reduced basis element method for the steady Stokes problem." ESAIM: Mathematical Modelling and Numerical Analysis 40.3 (2006): 529-552. <http://eudml.org/doc/249699>.

@article{Løvgren2006,

abstract = {
The reduced basis element method is a new approach for approximating
the solution of problems described by partial differential equations.
The method takes its roots in domain decomposition methods and
reduced basis discretizations. The basic idea is to first decompose
the computational domain into a series of subdomains that are deformations
of a few reference domains (or generic computational parts).
Associated with each reference domain are precomputed solutions
corresponding to the same governing partial differential equation,
but solved for different choices of deformations of the reference
subdomains and mapped onto the reference shape.
The approximation corresponding to a new shape is then taken
to be a linear combination of the precomputed solutions, mapped
from the generic computational part to the actual computational part.
We extend earlier work in this direction to solve incompressible
fluid flow problems governed by the steady Stokes equations.
Particular focus is given to satisfying the inf-sup condition,
to a posteriori error estimation,
and to “gluing” the local solutions together in the multidomain case.
},

author = {Løvgren, Alf Emil, Maday, Yvon, Rønquist, Einar M.},

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

keywords = {Stokes flow; reduced basis; reduced order model; domain decomposition; mortar method; output bounds; a posteriori error estimators.; a posteriori error estimator; inf-sup condition},

language = {eng},

month = {7},

number = {3},

pages = {529-552},

publisher = {EDP Sciences},

title = {A reduced basis element method for the steady Stokes problem},

url = {http://eudml.org/doc/249699},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Løvgren, Alf Emil

AU - Maday, Yvon

AU - Rønquist, Einar M.

TI - A reduced basis element method for the steady Stokes problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/7//

PB - EDP Sciences

VL - 40

IS - 3

SP - 529

EP - 552

AB -
The reduced basis element method is a new approach for approximating
the solution of problems described by partial differential equations.
The method takes its roots in domain decomposition methods and
reduced basis discretizations. The basic idea is to first decompose
the computational domain into a series of subdomains that are deformations
of a few reference domains (or generic computational parts).
Associated with each reference domain are precomputed solutions
corresponding to the same governing partial differential equation,
but solved for different choices of deformations of the reference
subdomains and mapped onto the reference shape.
The approximation corresponding to a new shape is then taken
to be a linear combination of the precomputed solutions, mapped
from the generic computational part to the actual computational part.
We extend earlier work in this direction to solve incompressible
fluid flow problems governed by the steady Stokes equations.
Particular focus is given to satisfying the inf-sup condition,
to a posteriori error estimation,
and to “gluing” the local solutions together in the multidomain case.

LA - eng

KW - Stokes flow; reduced basis; reduced order model; domain decomposition; mortar method; output bounds; a posteriori error estimators.; a posteriori error estimator; inf-sup condition

UR - http://eudml.org/doc/249699

ER -

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