Comptes Rendus
no. 3
Numerical Analysis
Finite elements for a prefractal transmission problem
[Éléments finis pour un problème de transmission préfractale]

Présenté par : Philippe G. Ciarlet

Patrizia Bagnerini1 ; Annalisa Buffa2 ; Elisa Vacca3
1 DIPTEM, Università degli Studi di Genova, P.le Kennedy-Pad D, 16129 Genova, Italy
2 Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento Me.Mo.Mat., Università degli Studi di Roma “La Sapienza”, Via Scarpa 16, 00161 Roma, Italy
Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 211-214.

Cette Note concerne l'approximation éléments finis d'un problème de transmission à travers la courbe préfractale approchant la courbe fractale de von Koch. On construit un maillage adapté à la géométrie de l'interface et on génère un processus de raffinement de maillage en utilisant des estimations dans des espaces de Sobolev à poids, choisis convenablement. On obtient aussi dans ces espaces une estimation de l'erreur d'approximation.

In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an approximation error estimate.

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DOI : 10.1016/j.crma.2005.11.023

Patrizia Bagnerini 1 ; Annalisa Buffa 2 ; Elisa Vacca 3

1 DIPTEM, Università degli Studi di Genova, P.le Kennedy-Pad D, 16129 Genova, Italy
2 Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento Me.Mo.Mat., Università degli Studi di Roma “La Sapienza”, Via Scarpa 16, 00161 Roma, Italy 
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Patrizia Bagnerini; Annalisa Buffa; Elisa Vacca. Finite elements for a prefractal transmission problem. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 211-214. doi : 10.1016/j.crma.2005.11.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.023/

[1] I. Babuška; R.B. Kellog; J. Pitkäranta Directe and inverse error estimates for finite elements with mesh refinements, Numer. Math., Volume 33 (1979), pp. 447-471

[2] F. Brezzi; G. Gilardi Finite elements mathematics (H. Kardestuncer; D.H. Norrie, eds.), Finite Element Handbook, MacGraw-Hill Book Co., New York, 1987

[3] P.G. Ciarlet Basic error estimates for elliptic problems (P.G. Ciarlet; J.L. Lions, eds.), Handbook of Numerical Analysis, North-Holland, Amsterdam, 1991, pp. 16-351

[4] M. Filoche; B. Sapoval Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett., Volume 84 (2000), pp. 5776-5779

[5] M.R. Lancia Second order transmission problem across a fractal surface, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5), Volume 27 (2003), pp. 191-213

[6] M.R. Lancia; M.A. Vivaldi On the regularity of the solutions for transmission problems, Adv. Math. Sci. Appl., Volume 12 (2002), pp. 455-466

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