On étudie quelques techniques simples de calcul des coefficients (‘moments’) des p-formes de Whitney de degré un sur les p-simplexes. On montre l'équivalence entre la méthode classique, de type métrique, pour le calcul de ces poids, et une méthode de type affine, mieux adaptée au contexte des formes différentielles.
We investigate some simple techniques of computation of the weights (‘moments’) of simplicial Whitney p-forms of first polynomial degree. The classical metric-dependent computation of weights is shown to be equivalent to an affine one, more suitable in the context of differential forms.
Accepté le :
Publié le :
Francesca Rapetti 1
@article{CRMATH_2005__341_8_519_0, author = {Francesca Rapetti}, title = {Weights computation for simplicial {Whitney} forms of degree one}, journal = {Comptes Rendus. Math\'ematique}, pages = {519--523}, publisher = {Elsevier}, volume = {341}, number = {8}, year = {2005}, doi = {10.1016/j.crma.2005.09.005}, language = {en}, }
Francesca Rapetti. Weights computation for simplicial Whitney forms of degree one. Comptes Rendus. Mathématique, Volume 341 (2005) no. 8, pp. 519-523. doi : 10.1016/j.crma.2005.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.005/
[1] Computational Electromagnetism, Academic Press, New York, 1998
[2] Géométrie de l'électromagnétisme et éléments finis (G. Meunier, ed.), Electromagnétisme et éléments finis, I.1, Hermès-Lavoisier, Paris, 2003, pp. 17-146
[3] A. Bossavit, F. Rapetti, A prolongation/restriction operator for Whitney elements on simplicial meshes, SIAM J. Numer. Anal. (2004), in press
[4] Finite Element Methods for Navier–Stokes Equations. Theory and Applications, Springer-Verlag, Berlin/New York, 1986
[5] Mixed finite elements in , Numer. Math., Volume 35 (1980), pp. 315-341
[6] A new family of mixed finite elements in , Numer. Math., Volume 35 (1986), pp. 57-81
[7] Domain Decomposition, Cambridge Univ. Press, Cambridge, UK, 1996
[8] Geometric Integration Theory, Princeton Univ. Press, 1957
[9] Functional Analysis, Springer-Verlag, Berlin/New York, 1980
Cité par Sources :
Commentaires - Politique