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We prove the accuracy of a mixed finite element method for bending dominatedshells in which a major part of the membrane/shear strain is reduced, to freeup membrane/shear locking. When no part of the membrane/shear strain isreduced, the method becomes a consistent discontinuous Galerkin method that isproven accurate for membrane/shear dominated shells and intermediate shells.The two methods can be coded in a single program by using a parameter. Wepropose a procedure of numerically detecting the asymptotic behavior of ashell, choosing the parameter value in the method, and producing accurateapproximation for a given shell problem. The method uses piecewise linearfunctions to approximate all the variables. The analysis is carried out forshells whose middle surfaces have the most general geometries, which shows thatthe method has the optimal order of accuracy for general shells and theaccuracy is robust with respect to the shell thickness. In the particular casethat the geometrical coefficients of the shell middle surface are piecewiseconstants the accuracy is uniform with respect to the shell thickness.

A linear finite element procedure for the Naghdi shell model