Raviart Thomas Petrov-Galerkin Finite Elements

The general theory of Babu\v{s}ka ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreover, the mixed method of Raviart-Thomas with low-level elements can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of type Petrov-Galerkin to ensure a local computation of the gradient at the interfaces of the elements. The in-depth study of stability leads to a specific choice of the test functions. With this choice, we show on the one hand that the mixed Petrov-Galerkin obtained is identical to the finite volumes scheme "volumes finis \`a 4 points" ("VF4") of Faille, Gallo\"uet and Herbin and to the condensation of mass approach developed by Baranger, Maitre and Oudin. On the other hand, we show the stability via an inf-sup condition and finally the convergence with the usual methods of mixed finite elements.Comment: arXiv admin note: text overlap with arXiv:1710.0439

Local time steps for a finite volume scheme

We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with piecewise constant projections and domain decomposition techniques. Next we present an iterative method for solving the composite-grid system that reduces to solution of standard problems with standard time stepping on the coarse and fine grids. At every step of the algorithm, conservativity is ensured. Finally, numerical results illustrate the accuracy of the proposed methods

Comparison of Demosaicking Methods for Color Information Extraction

Most digital color cameras are based on a single CCD or CMOS sensor combined with a color filter array (CFA): each pixel measures only one of the RGB colors. The most popular CFA is the Bayer CFA (Bayer, 1976) shown in fig. 1. Demosaicking algorithms interpolat

Découverte remarquable dans une grotte du sud-ouest du Maroc : Siagona taggadertensis n.sp. (Carabidae : Siagoninae)

[EN] Five species of the genus Siagona Latreille 1804 (Carabidae: Siagoninae) are known from Morocco. Siagona taggadertensis n. sp., a remarkable species of Carabidae from a Moroccan cave is described. This insect is spectacular by its large size (one of the largest species of the genus), its external morphology, which isolates it from all the north african representant of the genus, and for the conditions of its discovery: its only known from the remains of six specimens, all of them found in the cave of Taggadert, western Atlas. Hypotheses concerning the ecology of this species are discussed.[FR] Le genre Siagona Latreille 1804 (Carabidae: Siagoninae), compte 5 espèces au Maroc. Siagona taggadertensis n. sp., remarquable espèce collectée dans une grotte marocaine est décrite. Cet insecte est spectaculaire tant par sa grande taille, sa morphologie externe qui l’isole au premier coup d’oeil des représentants nord africains du genre Siagona, que par les conditions de sa découverte : aucun des spécimens n’ont été collectés en dehors de la grotte de Taggadert, Atlas occidental. Des hypothèses concernant l’écologie de cette espèce sont fournies.AF was supported by a postdoctoral Research Fellowship from the Alexander von Humboldt Foundation.Peer reviewe

A new microphthalmic stygobitic Graptodytes Seidlitz from Morocco, with a molecular phylogeny of the genus (Coleoptera, Dytiscidae)

14 páginas, 13 figuras, 2 tablas.-- Articulo Open Access.We describe Graptodytes eremitus n.sp. (Coleoptera, Dytiscidae), a depigmented, microphthalmic stygobitic species found in a pool in the deep area of a cave in the High Atlas of Morocco. To establish its phylogenetic position we inferred a molecular phylogeny of the genus Graptodytes Seidlitz, using ca. 1.7 Kb of four mitochondrial genes for 18 of the 23 previously known species and subspecies of the genus. Graptodytes can be separated in three well supported main lineages, 1) the G. flavipes lineage (apex of median lobe narrow in ventral view), 2) the G. granularis lineage (apex of median lobe expanded and strongly asymmetrical in ventral view), and 3) the G. varius lineage (apex of median lobe expanded but symmetrical in ventral view). The G. varius lineage includes the G. aequalis and G. varius groups, the latter including G. eremitus n.sp. as sister to G. delectus Wollaston (Canary Islands) plus the G. varius complex. A molecular clock approach, using a calibration rate of 2.3% divergence/MY for the combined mitochondrial sequence, estimated the origin of the diversification within the genus at ca. 7MY (late Miocene), and the origin of G. eremitus n.sp. at ca. 2 MY (Pliocene-Pleistocene boundary).This work was partly funded with projects CGL2004-00028 and CGL2007-61665 to IR.Peer reviewe