Geodesic
A posteriori error analysis for Poisson's equation approximated by XFEM
Patrick Hild1 ; Vanessa Lleras2 ; Yves Renard3
1 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, U niversité de Franche-Comté, 16 route de Gray, 25030 Besançon, France;
2 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France;
3 Institut Camille Jordan, UMR CNRS 5208, INSA de Lyon, 20 rue Albert Einstein, 69621 Villeurbanne, France;
ESAIM. Proceedings, Tome 27 (2009), pp. 107-121.

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This paper presents and studies a residual a posteriori error estimator for Laplace's equation in two space dimensions approximated by the eXtended Finite Element Method (XFEM). The XFEM allows to perform finite element computations on multi-cracked domains by using meshes of the non-cracked domain. The main idea consists of adding supplementary basis functions of Heaviside type and singular functions in order to take into account the crack geometry and the singularity at the crack tip respectively.
DOI : 10.1051/proc/2009022

Patrick Hild 1 ; Vanessa Lleras 2 ; Yves Renard 3

1 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, U niversité de Franche-Comté, 16 route de Gray, 25030 Besançon, France;
2 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France;
3 Institut Camille Jordan, UMR CNRS 5208, INSA de Lyon, 20 rue Albert Einstein, 69621 Villeurbanne, France; 
@article{EP_2009_27_a6,
     author = {Patrick Hild and Vanessa Lleras and Yves Renard},
     title = {A posteriori error analysis for {Poisson's} equation approximated by {XFEM}},
     journal = {ESAIM. Proceedings},
     pages = {107--121},
     publisher = {mathdoc},
     volume = {27},
     year = {2009},
     doi = {10.1051/proc/2009022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009022/}
}
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Patrick Hild; Vanessa Lleras; Yves Renard. A posteriori error analysis for Poisson's equation approximated by XFEM. ESAIM. Proceedings, Tome 27 (2009), pp. 107-121. doi : 10.1051/proc/2009022. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009022/

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