Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations

@article{Rozza2007ReducedBA,
  title={Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations},
  author={G. Rozza and D. Huynh and A. Patera},
  journal={Archives of Computational Methods in Engineering},
  year={2007},
  volume={15},
  pages={229-275}
}
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations… Expand
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation
In this paper we consider reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear and non-linear parabolic partial differentialExpand
Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinely parametrized geometries. The essential ingredientsExpand
Reduced basis approximation and error bounds for potential flows in parametrized geometries
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essentialExpand
REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS
In this paper we present reduced basis (RB) approximations and associated rigorous a posteriori error bounds for the parametrized unsteady Boussinesq equations. The essential ingredients are GalerkinExpand
Certified reduced basis methods for parametrized parabolic partial differential equations with non-affine source terms
Abstract We present rigorous a posteriori output error bounds for reduced basis approximations of parametrized parabolic partial differential equations with non-affine source terms. The methodExpand
A reduced basis method with exact-solution certificates for steady symmetric coercive equations
Abstract We introduce a reduced basis method that computes rigorous upper and lower bounds of the energy associated with the infinite-dimensional weak solution of parametrized steady symmetricExpand
REDUCED BASIS A POSTERIORI ERROR BOUNDS FOR THE STOKES EQUATIONS IN PARAMETRIZED DOMAINS: A PENALTY APPROACH
We present reduced basis approximations and associated rigorous a posteriori error bounds for the Stokes equations in parametrized domains. The method, built upon the penalty formulation for saddleExpand
Discontinuous Galerkin reduced basis empirical quadrature procedure for model reduction of parametrized nonlinear conservation laws
TLDR
The formulation for parametrized aerodynamics problems governed by the compressible Euler and Navier-Stokes equations is demonstrated, and a direct quantitative control of the solution error induced by the hyperreduction is provided. Expand
CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
We present reduced basis approximations and associated a posteriori error bounds for parabolic partial differential equations involving (i) a nonaffine dependence on the parameter and (ii ) aExpand
An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs
Abstract We present a model reduction formulation for parametrized nonlinear partial differential equations (PDEs). Our approach builds on two ingredients: reduced basis (RB) spaces which provideExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 193 REFERENCES
Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
Abstract We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of coercive elliptic partial differential equations with affine (input)Expand
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affineExpand
"Natural norm" a posteriori error estimators for reduced basis approximations
TLDR
A new "natural norm" formulation for the reduced basis error estimation framework is proposed that greatly simplifies and improves the inf-sup lower bound construction (offline) and evaluation (online) and significantly sharpens - the authors' output error bounds. Expand
A Posteriori Error Bounds for Reduced-Basis Approximation of Parametrized Noncoercive and Nonlinear Elliptic Partial Differential Equations
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine parameter dependence. The essential components are (i)Expand
Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity
We present an application in multi-parametrized sub-domains based on a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equationsExpand
Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essentialExpand
Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essentialExpand
A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for theExpand
REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS
The model order reduction methodology of reduced basis (RB) techniques offers efficient treatment of parametrized partial differential equations (P2 DEs) by providing both approximate solutionExpand
Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations
The model order reduction methodology of reduced basis (RB) techniques offers efficient treatment of parametrized partial differential equations (PDEs) by providing both approximate solutionExpand
...
1
2
3
4
5
...