Abstract:
In this work, we introduce an $$hp$$hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori error estimates and define a local a posteriori error estimator of residual type. We show, under appropriate assumptions about the curved domain, the global reliability and the local efficiency of the estimator. More precisely, we prove that the estimator is equivalent to the energy norm of the error up to higher-order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree. We also present an $$hp$$hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy. © 2014, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
Registro:
Documento: |
Artículo
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Título: | An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
Autor: | Armentano, M.G.; Padra, C.; Scheble, M. |
Filiación: | Departamento de Matemática, Universidad de Buenos Aires, IMAS-Conicet, Buenos Aires, 1428, Argentina Centro Atómico Bariloche, Bariloche, 4800, Argentina
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Palabras clave: | A posteriori error estimates; Curved domains; Finite elements; hp version |
Año: | 2015
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Volumen: | 34
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Número: | 2
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Página de inicio: | 705
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Página de fin: | 727
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DOI: |
http://dx.doi.org/10.1007/s40314-014-0133-z |
Título revista: | Computational and Applied Mathematics
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Título revista abreviado: | Comput. Appl. Math.
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ISSN: | 01018205
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01018205_v34_n2_p705_Armentano |
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Citas:
---------- APA ----------
Armentano, M.G., Padra, C. & Scheble, M.
(2015)
. An hp finite element adaptive scheme to solve the Poisson problem on curved domains. Computational and Applied Mathematics, 34(2), 705-727.
http://dx.doi.org/10.1007/s40314-014-0133-z---------- CHICAGO ----------
Armentano, M.G., Padra, C., Scheble, M.
"An hp finite element adaptive scheme to solve the Poisson problem on curved domains"
. Computational and Applied Mathematics 34, no. 2
(2015) : 705-727.
http://dx.doi.org/10.1007/s40314-014-0133-z---------- MLA ----------
Armentano, M.G., Padra, C., Scheble, M.
"An hp finite element adaptive scheme to solve the Poisson problem on curved domains"
. Computational and Applied Mathematics, vol. 34, no. 2, 2015, pp. 705-727.
http://dx.doi.org/10.1007/s40314-014-0133-z---------- VANCOUVER ----------
Armentano, M.G., Padra, C., Scheble, M. An hp finite element adaptive scheme to solve the Poisson problem on curved domains. Comput. Appl. Math. 2015;34(2):705-727.
http://dx.doi.org/10.1007/s40314-014-0133-z