On the approximation of stability factors for general
          parametrized partial differential equations with a two-level affine
          decomposition

Toni Lassila; Andrea Manzoni; Gianluigi Rozza

Displaying similar documents to “On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition”

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Toni Lassila, Andrea Manzoni, Gianluigi Rozza (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors,...

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Toni Lassila, Andrea Manzoni, Gianluigi Rozza (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method

Fabien Casenave, Alexandre Ern, Tony Lelièvre (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...

A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

Dinh Bao Phuong Huynh, David J. Knezevic, Anthony T. Patera (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric . The method is based on static condensation at the interdomain level, a conforming eigenfunction “port” representation...

Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods

Carsten Carstensen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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One of the main tools in the proof of residual-based error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed finite...