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Remarks on CR-manifolds of codimension 2 in C 4

Schmalz, Gerd — 1999

Proceedings of the 18th Winter School "Geometry and Physics"

The aim of the article is to give a conceptual understanding of Kontsevich’s construction of the universal element of the cohomology of the coarse moduli space of smooth algebraic curves with given genus and punctures. In a first step the author presents a toy model of tree graphs coloured by an operad 𝒫 for which the graph complex and the universal cycle will be constructed. The universal cycle has coefficients in the operad for Ω ( 𝒫 * ) -algebras with trivial differential over the (dual) cobar construction...

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

Gerd Kunert — 2001

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

Singularly perturbed problems often yield solutions with strong directional features, e.g. 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 anisotropic finite element...

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