We test the performance of standard finite element approximations of varying degree in three simple benchmark shell problems in cylindrical shell geometry. The exact solutions to these problems are computed both numerically and symbolically. We demonstrate by these problems that seemingly similar shell problems can be quite different in their mathematical character, and that this hidden diversity is strongly reflected in the performance of the standard low-order finite element methods. We also demonstrate that raising the degree of the elements as a rule highly improves the accuracy and makes the finite element scheme more robust.

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