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Finite element approximation of a prestressed shell model
Author(s) -
Rezzag Bara Rayhana,
Nicaise Serge,
Merabet Ismail
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6196
Subject(s) - mathematics , finite element method , shell (structure) , mixed finite element method , element (criminal law) , mathematical analysis , calculus (dental) , structural engineering , composite material , engineering , materials science , medicine , dentistry , political science , law
This work deals with the finite element approximation of a prestressed shell model formulated in Cartesian coordinates system. The considered constrained variational problem is not necessarily positive. Moreover, because of the constraint, it cannot be discretized by conforming finite element methods. A penalized version of the model and its discretization are then proposed. We prove existence and uniqueness results of solutions for the continuous and discrete problems, and we derive optimal a priori error estimates. Numerical tests that validate and illustrate our approach are given.