Convergence of some adaptive FEM-BEM coupling for elliptic but
          possibly nonlinear interface problems

Markus Aurada; Michael Feischl; Dirk Praetorius

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Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada, Michael Feischl, Dirk Praetorius (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new error estimators based on the ( − /2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive algorithm is ...

Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes

Gerd Kunert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Singularly perturbed problems often yield solutions with strong directional features, with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for finite element...

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 a posteriori error analysis for dynamic viscoelastic problems

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

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

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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...