On the asymptotic exactness of error estimators for linear triangular finite elements
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under...
| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
1991
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/134060 |
| Aporte de: |
| id |
I19-R120-10915-134060 |
|---|---|
| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Ciencias Exactas Matemática elliptic problems superconvergence error estimator |
| spellingShingle |
Ciencias Exactas Matemática elliptic problems superconvergence error estimator Durán, Ricardo Guillermo Muschietti, María Amelia Rodríguez, Rodolfo On the asymptotic exactness of error estimators for linear triangular finite elements |
| topic_facet |
Ciencias Exactas Matemática elliptic problems superconvergence error estimator |
| description |
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples. |
| format |
Articulo Articulo |
| author |
Durán, Ricardo Guillermo Muschietti, María Amelia Rodríguez, Rodolfo |
| author_facet |
Durán, Ricardo Guillermo Muschietti, María Amelia Rodríguez, Rodolfo |
| author_sort |
Durán, Ricardo Guillermo |
| title |
On the asymptotic exactness of error estimators for linear triangular finite elements |
| title_short |
On the asymptotic exactness of error estimators for linear triangular finite elements |
| title_full |
On the asymptotic exactness of error estimators for linear triangular finite elements |
| title_fullStr |
On the asymptotic exactness of error estimators for linear triangular finite elements |
| title_full_unstemmed |
On the asymptotic exactness of error estimators for linear triangular finite elements |
| title_sort |
on the asymptotic exactness of error estimators for linear triangular finite elements |
| publishDate |
1991 |
| url |
http://sedici.unlp.edu.ar/handle/10915/134060 |
| work_keys_str_mv |
AT duranricardoguillermo ontheasymptoticexactnessoferrorestimatorsforlineartriangularfiniteelements AT muschiettimariaamelia ontheasymptoticexactnessoferrorestimatorsforlineartriangularfiniteelements AT rodriguezrodolfo ontheasymptoticexactnessoferrorestimatorsforlineartriangularfiniteelements |
| bdutipo_str |
Repositorios |
| _version_ |
1764820455866236928 |