Artículo
Acostat, G.; Armentano, M.G.; Durán, R.G.; Lombardi, A.L. "Finite element approximations in a nonlipschitz domain" (2007) SIAM Journal on Numerical Analysis. 45(1):277-295
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Abstract:
In this paper we analyze the approximation by standard piecewise linear finite elements of a nonhomogeneous Neumann problem in a cuspidal domain. Since the domain is not Lipschitz, many of the results on Sobolev spaces, which are fundamental in the usual error analysis, do not apply. Therefore, we need to work with weighted Sobolev spaces and to develop some new theorems on traces and extensions. We show that, in the domain considered here, suboptimal order can be obtained with quasi-uniform meshes even when the exact solution is in H 2, and we prove that the optimal order with respect to the number of nodes can be recovered by using appropriate graded meshes. © 2007 Society for Industrial and Applied Mathematics.
Registro:
| Documento: | Artículo |
| Título: | Finite element approximations in a nonlipschitz domain |
| Autor: | Acostat, G.; Armentano, M.G.; Durán, R.G.; Lombardi, A.L. |
| Filiación: | Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Pab. I, Argentina CONICET, Argentina |
| Palabras clave: | Cuspidal domains; Finite elements; Graded meshes; Neumann problem; Error analysis; Finite element method; Problem solving; Cuspidal domains; Graded meshes; Neumann problem; Approximation algorithms |
| Año: | 2007 |
| Volumen: | 45 |
| Número: | 1 |
| Página de inicio: | 277 |
| Página de fin: | 295 |
| DOI: | http://dx.doi.org/10.1137/050647797 |
| Título revista: | SIAM Journal on Numerical Analysis |
| Título revista abreviado: | SIAM J Numer Anal |
| ISSN: | 00361429 |
| CODEN: | SJNAA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v45_n1_p277_Acostat |
Referencias:
- ACOSTA, G., ARMENTANO, M.G., DURÁN, R.G., LOMBARDI, A.L., Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp (2005) J. Math. Anal. Appl, 310, pp. 397-411
- ADAMS, R.A., (1975) Sobolev Spaces, , Academic Press, New York
- T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., B. G. Teubner, Stuttgart, 1999; BABUSǨA, I., KELLOG, R.B., PITKARANTA, J., Direct and inverse error estimates for finite elements with mesh refinements (1979) Numer. Math, 33, pp. 447-471
- BRAMBLE, J.H., KING, J.T., A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries (1994) Math. Comp, 63, pp. 1-17
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- HARDY, G., LITTLEWOOD, J.E., POLYA, G., (1952) Inequalities, , Cambridge University Press, Cambridge, UK
- RAUGEL, G., Résolution numérique par une méthode d'éléments finis du problème Dirichlet pour le laplacien dans un polygone (1978) C. R. Acad, Sci. Paris Ser. A, 286, pp. A791-A794
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Citas:
---------- APA ----------
Acostat, G., Armentano, M.G., Durán, R.G. & Lombardi, A.L. (2007) . Finite element approximations in a nonlipschitz domain. SIAM Journal on Numerical Analysis, 45(1), 277-295.http://dx.doi.org/10.1137/050647797
---------- CHICAGO ----------
Acostat, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. "Finite element approximations in a nonlipschitz domain" . SIAM Journal on Numerical Analysis 45, no. 1 (2007) : 277-295.http://dx.doi.org/10.1137/050647797
---------- MLA ----------
Acostat, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. "Finite element approximations in a nonlipschitz domain" . SIAM Journal on Numerical Analysis, vol. 45, no. 1, 2007, pp. 277-295.http://dx.doi.org/10.1137/050647797
---------- VANCOUVER ----------
Acostat, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. Finite element approximations in a nonlipschitz domain. SIAM J Numer Anal. 2007;45(1):277-295.http://dx.doi.org/10.1137/050647797
