  We propose a mixed discontinuous Galerkin method for the bending problem of
Naghdi shell, and present an analysis for its accuracy. The error estimate
shows that when components of the curvature tensor and Christoffel symbols are
piecewise linear functions, the finite element method has the optimal order of
accuracy, which is uniform with respect to the shell thickness. Generally, the
error estimate shows how the accuracy is affected by the shell geometry and
thickness. It suggests that to achieve optimal rate of convergence, the
triangulation should be properly refined in regions where the shell geometry
changes dramatically. These are the results for a balanced method in which the
primary displacement components and rotation components are approximated by
discontinuous piecewise quadratic polynomials, while components of the scaled
membrane stress tensor and shear stress vector are approximated by continuous
piecewise linear functions. On elements that have edges on the free boundary of
the shell, finite element space for displacement components needs to be
enriched slightly, for stability purpose. Results on higher order finite
elements are also included.
