Soon Capturing and Frequency Analysis for Mesh Adaptive Interpolation

Bernadette Palmerio 1 Alain Dervieux
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
Type de document :
Rapport
RR-2722, INRIA. 1995
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https://hal.inria.fr/inria-00073971
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Soumis le : mercredi 24 mai 2006 - 14:12:25
Dernière modification le : samedi 27 janvier 2018 - 01:31:30
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Bernadette Palmerio, Alain Dervieux. Soon Capturing and Frequency Analysis for Mesh Adaptive Interpolation. RR-2722, INRIA. 1995. 〈inria-00073971〉

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