An hp finite element adaptive scheme to solve the Poisson problem on curved domains
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 doma...
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2015
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01018205_v34_n2_p705_Armentano http://hdl.handle.net/20.500.12110/paper_01018205_v34_n2_p705_Armentano |
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paper:paper_01018205_v34_n2_p705_Armentano2023-06-08T15:10:18Z An hp finite element adaptive scheme to solve the Poisson problem on curved domains A posteriori error estimates Curved domains Finite elements hp version 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. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01018205_v34_n2_p705_Armentano http://hdl.handle.net/20.500.12110/paper_01018205_v34_n2_p705_Armentano |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
A posteriori error estimates Curved domains Finite elements hp version |
| spellingShingle |
A posteriori error estimates Curved domains Finite elements hp version An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| topic_facet |
A posteriori error estimates Curved domains Finite elements hp version |
| description |
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. |
| title |
An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| title_short |
An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| title_full |
An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| title_fullStr |
An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| title_full_unstemmed |
An hp finite element adaptive scheme to solve the Poisson problem on curved domains |
| title_sort |
hp finite element adaptive scheme to solve the poisson problem on curved domains |
| publishDate |
2015 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01018205_v34_n2_p705_Armentano http://hdl.handle.net/20.500.12110/paper_01018205_v34_n2_p705_Armentano |
| _version_ |
1768545732194729984 |