A priori and a posteriori error analysis for a hybrid formulation of a
prestressed shell model.
Abstract
This work deals with the finite element approximation of a prestressed
shell model 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 confirmthe efficiency of our residual a posteriori
estimator.