A Posteriori Error Bounds for the Empirical Interpolation Method

By Jens L. Eftang, Martin A. Grepl, Anthony T. Patera. 2010

69 citations recorded by the source corpus.

We present rigorous a posteriori error bounds for the Empirical Interpolation Method (EIM). The essential ingredients are (i) analytical upper bounds for the parametric derivatives of the function to be approximated, (ii) the EIM \Lebesgue constant," and (iii) information concerning the EIM approximation error at a nite set of points in parameter space. The bound is computed \oine" and is valid over the entire parameter domain; it is thus readily employed in (say) the \online" reduced basis context. We present numerical results that conrm the

Subfields: Mathematical Physics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba38d4b2459b1156ea780b0dbb6094dfba4ecf4f

How researchers see this paper

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

In Mathematical Physics

1. Gianluigi Rozza
2. Benjamin Stamm
3. Paolo Pacciarini
4. Andrea Manzoni
5. Alfio Maria Quarteroni
6. Jens L. Eftang

In Mechanics of Materials

1. Andrea Manzoni
2. S. Kristoffersen
3. Alfio Maria Quarteroni
4. Benjamin Stamm
5. Gianluigi Rozza
6. Jens L. Eftang
7. Paolo Pacciarini
8. Bernhard Wieland

In Statistical and Nonlinear Physics

1. Andrea Manzoni
2. Gianluigi Rozza
3. Alfio Maria Quarteroni
4. Paolo Pacciarini
5. S. Kristoffersen
6. Benjamin Stamm
7. Jens L. Eftang
8. Anthony T. Patera

Citations in the corpus

• The Empirical Interpolation Method (2013, background): “A rigorous upper bound of the interpolation error was presented in [8].”
• Parameter multi‐domain ‘hp’ empirical interpolation (2012, methodology): “The hp-EIM method may also provide an improvement of the rigorous a posteriori error bounds recently introduced for the EIM [13].”
• Stabilized reduced basis method for parametrized advection-diffusion PDEs (2014, methodology): “empirical interpolation method) in order to recover the “affinity” assumption [1, 10,16,34].”
• An hp certified reduced basis method for parametrized parabolic partial differential equations (2011, unknown): “article) admit an affine expansion; for other problems, approximate affine representations can be developed [13,14].”
• Certified reduced basis approximation for parametrized partial differential equations and applications (2011, methodology): “At the same time, (i) improvements in the a posteriori error bounds for non-affine problems [38]; (ii) reduction of the complexity of the parametrized operators and more efficient estimation of lower bounds of stability factors (i.”