A DPG method for shallow shells

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