Artículo
Dari, E.; Durán, R.G.; Padra, C. "Maximum norm error estimators for three-dimensional elliptic problems" (2000) SIAM Journal on Numerical Analysis. 37(2):683-700
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Abstract:
In this paper we define an a posteriori error estimator for finite element approximations of 3-d elliptic problems. We prove that the estimator is equivalent, up to logarithmic factors of the meshsize, to the maximum norm of the error. The results are valid for an arbitrary polyhedral domain and rather general meshes. We also obtain analogous results for the nonconforming method of Crouzeix-Raviart. Finally, we present some numerical results comparing adaptive procedures based on controlling the error in different norms.
Registro:
| Documento: | Artículo |
| Título: | Maximum norm error estimators for three-dimensional elliptic problems |
| Autor: | Dari, E.; Durán, R.G.; Padra, C. |
| Filiación: | Centro Atómico Bariloche, CNEA, 8400 Bariloche, Rio Negro, Argentina Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina |
| Palabras clave: | A posteriori; Adaptivity; Error estimators; Maximum norm |
| Año: | 2000 |
| Volumen: | 37 |
| Número: | 2 |
| Página de inicio: | 683 |
| Página de fin: | 700 |
| 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_v37_n2_p683_Dari |
Referencias:
- Agmon, S., Douglis, A., Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions (1959) Comm. Pure Appl. Math., 12, pp. 623-727
- Babuška, I., Kellogg, R.B., Pitkäranta, J., Direct and inverse error estimates for finite elements with mesh refinements (1972) Numer. Math., 33, pp. 447-471
- Buscaglia, G., Dari, E.A., Anisotropic mesh optimization and its application in adaptivity (1997) Internat. J. Numer. Methods Engrg., 40, pp. 4119-4136
- Ciarlet, P.G., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam
- Clément, P., (1975) Approximation by Finite Element Function Using Local Regularization, 9, pp. 77-84. , Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér
- Crouzeix, M., Raviart, P.-A., (1973) Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations, 7, pp. 33-76. , Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér
- Dari, E., Durán, R., Padra, C., Vampa, V., A posteriori error estimators for nonconforming finite element methods (1996) RAIRO Modél. Math. Anal. Numér., 30, pp. 385-400
- Dari, E., Durán, R., Padra, C., Error estimators for nonconforming finite elements approximations of the Stokes problem (1995) Math. Comp., 64, pp. 1017-1033
- Dauge, M., Problèmes de Neumann et de Dirichlet sur un polyèdre dans ℝ3: Régularité dans des espaces de Sobolev Lp (1988) C. R. Acad. Sci. Paris Sér. i Math., 307, pp. 27-32
- Eriksson, K., An adaptive finite element method with efficient maximum norm error control for elliptic problems (1994) Math. Models Methods Appl. Sci., 4, pp. 313-329
- Gilbarg, D., Trudinger, N.S., (1983) Elliptic Partial Differential Equations of Second Order, , Springer-Verlag, Berlin
- Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domains, , Pitman, Boston, MA
- Hoppe, R., Wohlmuth, B., Element-oriented and edge-oriented local error estimators for nonconforming finite element methods (1996) RAIRO Modél Math. Anal. Numér., 30, pp. 237-263
- Jackson, J.D., (1975) Classical Electrodynamics, 2nd Ed., , John Wiley, New York
- Nochetto, R., Pointwise a posteriori error estimates for elliptic problems on highly graded meshes (1995) Math. Comp., 64, pp. 1-22
- Padra, C., A posteriori error estimators for nonconforming approximation of some quasi-newtonian flows (1997) SIAM J. Numer. Anal., 34, pp. 1600-1615
- Rivara, M.C., Mesh refinement processes based on the generalized bisection of simplices (1984) SIAM J. Numer. Anal., 21, pp. 604-613
- Scott, L.R., Zhang, S., Finite element interpolation of non-smooth functions satisfying boundary conditions (1990) Math. Comp., 54, pp. 483-493
- Schatz, A.H., Wahlbin, L.B., Maximum norm estimates in the finite element method on plane polygonal domains, Part 2, Refinements (1979) Math. Comp., 33, pp. 465-492
- Verfürth, R., A posteriori error estimators for the Stokes equations (1989) Numer. Math., 55, pp. 309-325
- Wahlbin, L.B., Local behavior in finite element methods (1991) Handbook of Numerical Analysis, 2, pp. 353-522. , P. G. Ciarlet, J. L. Lions, eds., North-Holland, Amsterdam
Citas:
---------- APA ----------
Dari, E., Durán, R.G. & Padra, C. (2000) . Maximum norm error estimators for three-dimensional elliptic problems. SIAM Journal on Numerical Analysis, 37(2), 683-700.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n2_p683_Dari [ ]
---------- CHICAGO ----------
Dari, E., Durán, R.G., Padra, C. "Maximum norm error estimators for three-dimensional elliptic problems" . SIAM Journal on Numerical Analysis 37, no. 2 (2000) : 683-700.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n2_p683_Dari [ ]
---------- MLA ----------
Dari, E., Durán, R.G., Padra, C. "Maximum norm error estimators for three-dimensional elliptic problems" . SIAM Journal on Numerical Analysis, vol. 37, no. 2, 2000, pp. 683-700.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n2_p683_Dari [ ]
---------- VANCOUVER ----------
Dari, E., Durán, R.G., Padra, C. Maximum norm error estimators for three-dimensional elliptic problems. SIAM J Numer Anal. 2000;37(2):683-700.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n2_p683_Dari [ ]
