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Remarks and examples concerning distance ellipsoids

Dirk Praetorius — 2002

Colloquium Mathematicae

We provide for every 2 ≤ k ≤ n an n-dimensional Banach space E with a unique distance ellipsoid such that there are precisely k linearly independent contact points between and B E . The corresponding result holds for spaces with non-unique distance ellipsoids as well. We construct n-dimensional Banach spaces E such that one distance ellipsoid has precisely k linearly independent contact points and all other distance ellipsoids have less than k-1 such points.

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

Markus AuradaMichael FeischlDirk Praetorius — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

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 ...

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

Markus AuradaMichael FeischlDirk Praetorius — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

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 ...

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