Reduced-basis output bound methods for parabolic problems

By Dimitrios Rovas, L. Machiels, Yvon Maday. 2006

76 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/64e2dbcc7f9712ba5d6cf212efe9f0910db7046c

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS (2008, methodology): “Time-dependency of problems is addressed for linear parabolic equations with finite difference time discretization in [15] and more general discontinuous Galerkin time integration in [35].”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “In particular, in Part IV we extend to parabolic PDEs the primal-dual approximations, greedy sampling strategies, a posteriori error estimation concepts, and Offline-Online computational strategies developed in Part II for elliptic PDEs — with particular focus on the accommodation of an “evolution” ”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, background): “The exploration of the “parameter + time” framework in the important context of affine linear (stable) parabolic PDEs — such as the heat equation and the passive scalar convection-diffusion equation (also the Black-Scholes equation of derivative theory [118]) — is carried out in [52,55,60, 133 ]; ma”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, methodology): “The reduced basis [20, 21, 23, 24, 27] and the proper orthogonal decomposition (POD) [12,15, 17, 19, 28] are two techniques belonging to this second family.”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, background): “2 Concurrently with our submission, Rovas, Machiels, and Maday submitted a manuscript [38] summarizing the earlier work [39].”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, background): “Although there is no existence nor convergence results about the proposed definition (in the general case), it appears to be an 8 Let us also mention the “Reduced Basis Method” [35,7] as an alternative to POD for the definition of optimal reduced basis in the context of parametric or direct stochast”
Proper orthogonal decomposition for optimality systems (2008, background): “In this respect, reduced-basis elements [7, 20] offer an interesting alternative.”
Reduced basis methods for partial differential equations with stochastic influences (2013, background): “Besides linear elliptic [73, 77] and parabolic equations [40, 76], also more complicated quadratically nonlinear problems have been reduced [24, 86, 96].”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, unknown): “The reduced basis method and related model-reduction approaches are well developed for linear parametrized parabolic partial differential equations [10, 12, 15, 30, 34 ].”