This work deals with the finite element approximation of a prestressed shell model in the case of isometrically deformed shell. Using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirm the efficiency of our residual a posteriori estimator.
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@article{CML_2022__14_2_53_0,
author = {Serge Nicaise and Ismael Merabet and Rihana Rezzag Bara},
title = {A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model},
journal = {Confluentes Mathematici},
pages = {53--86},
publisher = {Institut Camille Jordan},
volume = {14},
number = {2},
year = {2022},
doi = {10.5802/cml.87},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.87/}
}
TY - JOUR AU - Serge Nicaise AU - Ismael Merabet AU - Rihana Rezzag Bara TI - A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model JO - Confluentes Mathematici PY - 2022 SP - 53 EP - 86 VL - 14 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.87/ DO - 10.5802/cml.87 LA - en ID - CML_2022__14_2_53_0 ER -
%0 Journal Article %A Serge Nicaise %A Ismael Merabet %A Rihana Rezzag Bara %T A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model %J Confluentes Mathematici %D 2022 %P 53-86 %V 14 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.87/ %R 10.5802/cml.87 %G en %F CML_2022__14_2_53_0
Serge Nicaise; Ismael Merabet; Rihana Rezzag Bara. A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model. Confluentes Mathematici, Tome 14 (2022) no. 2, pp. 53-86. doi : 10.5802/cml.87. https://cml.centre-mersenne.org/articles/10.5802/cml.87/
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