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nonlinear pdes

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Certified reduced-basis solutions of viscous Burgers equationparametrized by initial and boundary values
Alexandre Janon, Maëlle Nodet, Clémentine Prieur
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 2 / March 2013

Published online by Cambridge University Press:

11 January 2013, pp. 317-348

Print publication:

March 2013
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We present a reduced basis offline/online procedure for viscous Burgers initial boundaryvalue problem, enabling efficient approximate computation of the solutions of thisequation for parametrized viscosity and initial and boundary value data. This procedurecomes with a fast-evaluated rigorous error bound certifying the approximation procedure.Our numerical experiments show significant computational savings, as well as efficiency ofthe error bound.