HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

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.
Document type :
Complete list of metadata

Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 2:12:25 PM
Last modification on : Friday, February 4, 2022 - 3:15:09 AM
Long-term archiving on: : Thursday, March 24, 2011 - 1:34:04 PM


  • HAL Id : inria-00073971, version 1



Bernadette Palmerio, Alain Dervieux. Soon Capturing and Frequency Analysis for Mesh Adaptive Interpolation. RR-2722, INRIA. 1995. ⟨inria-00073971⟩



Record views


Files downloads