A DPG method for shallow shells
Thomas Führer, Norbert Heuer, and Antti H. Niemi
Numer. Math. 152 (1), 67–99, 2022.
We develop and analyze a discontinuous Petrov–Galerkin method with
optimal test functions (DPG method) for a shallow shell model of Koiter type.
It is based on a uniformly stable ultraweak formulation and thus converges
robustly quasi-uniformly. Numerical experiments for various cases, including
the Scordelis–Lo cylindrical roof, elliptic and hyperbolic geometries,
illustrate its performance. The built-in DPG error estimator gives rise to
adaptive mesh refinements that are capable to resolve boundary and interior
layers. The membrane locking is dealt with by raising the polynomial degree
only of the tangential displacement trace variable.