A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

Journal of Computational Physics ◽

10.1016/j.jcp.2007.08.031 ◽

2007 ◽

Vol 227 (2) ◽

pp. 983-1006 ◽

Author(s):

N.C. Nguyen

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

Elliptic Partial Differential Equations ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Reduced Basis ◽

A Posteriori Error

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

Archives of Computational Methods in Engineering ◽

10.1007/s11831-008-9019-9 ◽

2008 ◽

Vol 15 (3) ◽

pp. 229-275 ◽

Author(s):

G. Rozza ◽

D. B. P. Huynh ◽

A. T. Patera

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Reduced Basis ◽

Partial Differential ◽

A Posteriori Error

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Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations

Archives of Computational Methods in Engineering ◽

10.1007/bf03024948 ◽

2007 ◽

Vol 15 (3) ◽

pp. 1-47 ◽

Author(s):

G. Rozza ◽

D. B. P. Huynh ◽

A. T. Patera

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Reduced Basis ◽

Partial Differential ◽

A Posteriori Error

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Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

10.21236/ada563403 ◽

2010 ◽

Author(s):

Jan S. Hesthaven ◽

Anthony T. Patera

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Reduced Basis ◽

A Posteriori Error ◽

Parametrized Partial Differential Equations

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A posteriori error estimation for elliptic partial differential equations with small uncertainties

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21991 ◽

2015 ◽

Vol 32 (1) ◽

pp. 175-212 ◽

Author(s):

Diane Guignard ◽

Fabio Nobile ◽

Marco Picasso

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

Elliptic Partial Differential Equations ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Partial Differential ◽

A Posteriori Error

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A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations

Numerische Mathematik ◽

10.1007/s00211-009-0285-8 ◽

2010 ◽

Vol 115 (3) ◽

pp. 475-509 ◽

Author(s):

Dominik Schötzau ◽

Thomas P. Wihler

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

Parabolic Partial Differential Equations ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error ◽

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A-posteriori error estimation for finite element modifications of line methods applied to singularly perturbed partial differential equations

Applied Numerical Mathematics ◽

10.1016/0168-9274(85)90022-4 ◽

1985 ◽

Vol 1 (2) ◽

pp. 145-176 ◽

Author(s):

Hans-Jürgen Reinhardt

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

Singularly Perturbed ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error

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A posteriori error estimation methods for partial differential equations

Lectures on Advanced Computational Methods in Mechanics ◽

10.1515/9783110927092.161 ◽

2007 ◽

pp. 161-228

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

Estimation Methods ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Partial Differential ◽

A Posteriori Error

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A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(00)00340-6 ◽

2001 ◽

Vol 190 (35-36) ◽

pp. 4691-4712 ◽

Author(s):

I. Babuška ◽

S. Ohnimus

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Differential Equations ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Parabolic Differential Equations ◽

A Posteriori Error

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A Posteriori Error Bounds for Reduced-Basis Approximation of Parametrized Noncoercive and Nonlinear Elliptic Partial Differential Equations

16th AIAA Computational Fluid Dynamics Conference ◽

10.2514/6.2003-3847 ◽

2003 ◽

Author(s):

Karen Veroy ◽

Christophe Prud'homme ◽

Dimitrios Rovas ◽

Anthony Patera

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Error Bounds ◽

Posteriori Error ◽

Elliptic Partial Differential Equations ◽

A Posteriori ◽

Reduced Basis ◽

A Posteriori Error ◽

Nonlinear Elliptic ◽

A Posteriori Error Bounds

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Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real-Time Bayesian Parameter Estimation

Large-Scale Inverse Problems and Quantification of Uncertainty ◽

10.1002/9780470685853.ch8 ◽

2010 ◽

pp. 151-177 ◽

Author(s):

N. C. Nguyen ◽

G. Rozza ◽

D. B. P. Huynh ◽

A. T. Patera

Keyword(s):

Parameter Estimation ◽

Real Time ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

Reduced Basis ◽

Parabolic Pdes ◽

A Posteriori Error

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