Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations

Optimization and Engineering ◽

10.1007/s11081-007-9002-6 ◽

2007 ◽

Vol 8 (1) ◽

pp. 43-65 ◽

Author(s):

I. B. Oliveira ◽

A. T. Patera

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Reduced Basis ◽

Partial Differential

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Preconditioning Techniques for Reduced Basis Methods for Parameterized Elliptic Partial Differential Equations

SIAM Journal on Scientific Computing ◽

10.1137/140970859 ◽

2015 ◽

Vol 37 (5) ◽

pp. S177-S194 ◽

Author(s):

Howard C. Elman ◽

Virginia Forstall

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Reduced Basis ◽

Partial Differential ◽

Preconditioning Techniques ◽

Reduced Basis Methods

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A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales

Journal of Computational Physics ◽

10.1016/j.jcp.2008.07.025 ◽

2008 ◽

Vol 227 (23) ◽

pp. 9807-9822 ◽

Author(s):

N.C. Nguyen

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Multiple Scales ◽

Elliptic Partial Differential Equations ◽

Reduced Basis Method ◽

Reduced Basis ◽

Partial Differential ◽

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A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data

SIAM Journal on Numerical Analysis ◽

10.1137/130905253 ◽

2013 ◽

Vol 51 (6) ◽

pp. 3163-3185 ◽

Author(s):

Peng Chen ◽

Alfio Quarteroni ◽

Gianluigi Rozza

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Reduced Basis Method ◽

Random Input ◽

Reduced Basis ◽

Partial Differential ◽

Basis Method ◽

Random Input Data

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Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations

Comptes Rendus Mathematique ◽

10.1016/s1631-073x(02)02466-4 ◽

2002 ◽

Vol 335 (3) ◽

pp. 289-294 ◽

Author(s):

Yvon Maday ◽

Anthony T. Patera ◽

G. Turinici

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

A Priori ◽

Elliptic Partial Differential Equations ◽

Single Parameter ◽

Convergence Theory ◽

Reduced Basis ◽

Partial Differential

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An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations

SIAM Journal on Scientific Computing ◽

10.1137/090780122 ◽

2010 ◽

Vol 32 (6) ◽

pp. 3170-3200 ◽

Author(s):

Jens L. Eftang ◽

Anthony T. Patera ◽

Einar M. Rønquist

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Reduced Basis Method ◽

Reduced Basis ◽

Partial Differential ◽

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A priori estimates for solutions of elliptic partial differential equations on surfaces

10.32469/10355/10133 ◽

2009 ◽

Author(s):

Heidi Steenblock

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

A Priori Estimates ◽

A Priori ◽

Elliptic Partial Differential Equations ◽

Partial Differential ◽

Priori Estimates

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NOTE ON THE SOBOLEV'S THEOREM AND ITS APPLICATION TO THE LOCAL ESTIMATES FOR GENERALIZED SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Memoirs of the Faculty of Science Kyushu University Series A Mathematics ◽

10.2206/kyushumfs.20.56 ◽

1966 ◽

Vol 20 (1) ◽

pp. 56-60

Author(s):

Akira ONO

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Generalized Solutions ◽

Partial Differential

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Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/140971890 ◽

2015 ◽

Vol 53 (1) ◽

pp. 405-420 ◽

Author(s):

Zhiqiang Cai ◽

Rob Falgout ◽

Shun Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Second Order ◽

Order System ◽

Partial Differential ◽

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Transformation of elliptic partial differential equations for solving two-dimensional boundary value problems in fluid flow

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1620100304 ◽

1976 ◽

Vol 10 (3) ◽

pp. 527-533 ◽

Author(s):

J. D. Boadway

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Elliptic Partial Differential Equations ◽

Two Dimensional ◽

Partial Differential ◽

Dimensional Boundary

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Adams type inequalities and related elliptic partial differential equations in dimension four

Journal of Differential Equations ◽

10.1016/j.jde.2011.08.027 ◽

2012 ◽

Vol 252 (3) ◽

pp. 2266-2295 ◽

Author(s):

Yunyan Yang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Partial Differential

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