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inria-00073971, version 1

## Soon Capturing and Frequency Analysis for Mesh Adaptive Interpolation

Bernadette Palmerio 1, Alain Dervieux ()

N° RR-2722 (1995)

Résumé : Let us call a {\bf highly heterogeneous function} a function that is either locally singular or a smooth function but, with too small details in comparison with domain size. We study the $L^2$ norm of the interpolation error $E_h$ between a function $u$ and $\Pi_h$ $u$ its $P1$ continuous interpolate: we use four examples of functions, that represent different cases of {\bf highly heterogeneous functions}. Comparing first the convergence of $E_h$ as a function of number of nodes on uniform or adaptive meshes, we observe a convergence of order 2, only for a smooth function when the number of nodes is sufficiently large, when an uniform sequence of mesh is choosen. Conversely, almost always holds second-order convergence when an adaptive mesh algorithm is applied. We give some theoretical arguments concerning this phenomenon. Following some ideas currently used in spectral methods, we consider the $P1$ approximation of $u$ on nested meshes and express the representation of $u_h$ as a {\bf series} with increasing fineness of its terms. The size of each terms as a function of the corresponding level number is examined.

• 1 :  SINUS (INRIA Sophia Antipolis)
• INRIA
• Domaine : Informatique/Autre
• Mots-clés : FINITE ELEMENTS / $P1$ INTERPOLATION / CONVERGENCE / MESH ADAPTIVE METHOD / CRITERION / SPRING SYSTEM
• Référence interne : RR-2722

• inria-00073971, version 1
• oai:hal.inria.fr:inria-00073971
• Contributeur :
• Soumis le : Mercredi 24 Mai 2006, 14:12:25
• Dernière modification le : Mercredi 31 Mai 2006, 14:24:28