Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations

By Christophe Prud'Homme, Dimitrios Rovas, Karen Veroy, L. Machiels, Yvon Maday, Anthony T. Patera, Gabriel Turinici. 2002

95 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e3dd25a9657dc5d544b6e4bbe0b70d300b459c59

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Citations in the corpus

Numerical solution of parametrized Navier–Stokes equations by reduced basis methods (2007, methodology): “We now use the so-called supremizer solutions to enrich YN (as done for example in Rovas [23] and Patera et al. [15]).”
Reduced basis methods for partial differential equations with stochastic influences (2013, background): “, saddle point problems and especially the Stokes equations, RB theory has been introduced [33, 34, 75].”
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space (2008, methodology): “If a tight output error bound exists, it could be used as the cost functional instead of the true output error [15, 27, 32].”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, background): “Our approach here is a simplification and generalization of earlier efforts in this direction [39].”
Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity (2005, unknown): “See recent developments in [18].”
Reduced-basis output bound methods for parabolic problems (2006, background): “Both the a priori theory [13] (in the context of elliptic problems) and extensive numerical tests [16, 19] suggest that the points should be chosen “log-randomly” over D: we sample from a multivariate uniform probability density on log(D).”
On the stability of the reduced basis method for Stokes equations in parametrized domains (2007, unknown): “For further considerations on supremizer operator and the reduced basis framework, see [25] for the general non-coercive problem and [34] especially for Helmholtz and Burgers equations.”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, background): “Finally, a third question, again related to generality: What class of PDEs can be treated? In addition to the elliptic equations discussed in this paper, parabolic equations can also be addressed satisfactorily from both the approximation and error estimation points of view [24, 34, 35]:† much of th”