Displaying similar documents to “A Reduced Basis Enrichment for the eXtended Finite Element Method”

Error Estimates with Post-Processing for Nonconforming Finite Elements

Friedhelm Schieweck (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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For a nonconforming finite element approximation of an elliptic model problem, we propose error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is...

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

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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...

An error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error...