A blackbox reduced-basis output bound method for noncoercive linear problems

By Yvon Maday, Anthony T. Patera, Dimitrios Rovas. 2002

95 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e33df9c08dad837109e18d1a213494d2567db873

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations (2002, background): “In other cases, however, there is no self-evident (or readily computed [68]) good choice.”
Sparse-grid, reduced-basis Bayesian inversion (2015, methodology): “As the posterior density Θ(y) is nonlinear with respect to the parametric forward solution map q(y), we may not directly apply a primal-dual approach as in[36, 42].”
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space (2008, methodology): “Recently, the minimum-residual approach has been successfully used in the reduced-basis context [23, 27, 28].”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, methodology): “In the more recent past the reduced-basis approach and in particular associated a posteriori error estimation procedures have been successfully developed for (non)linear and (non)coercive elliptic PDEs with affine parameter dependence [23,34,41–43]; in this paper, we consider the extension of these ”
Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations (2002, result): “We refer also to [5, 6, 7, 12] for further discussions of these results and related work and applications.”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, background): “We next introduce [12, 18] the operator T μ : X→ X such that, for any w in X , (T w, v)X = a(w, v ; μ), ∀ v ∈ X .”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “In relation to Part II, the key new methodological elements are the development of (i) discretely stable primal-dual RB approximations [89], (ii) an efficient Offline-Online computational procedure [62, 139] for the construction of a lower bound for the general inf-sup constant [9] required by our a”
A parameterized‐background data‐weak approach to variational data assimilation: formulation, analysis, and application to acoustics (2015, unknown): “∆ N ≡ infw∈ZN supv∈UN |G(w, v)|/‖v‖ (see [21] for details).”