An ultraweak variational formulation with DPG approximation is developed for nondivergence-form elliptic PDEs with Cordes coefficients, with well-posedness, quasi-optimality, Fortin operators, and a posteriori estimators.
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
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abstract
We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness $t$. We also prove weak convergence of the Reissner-Mindlin solution to the solution of the corresponding Kirchhoff-Love model when $t\to 0$. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.
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Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation
An ultraweak variational formulation with DPG approximation is developed for nondivergence-form elliptic PDEs with Cordes coefficients, with well-posedness, quasi-optimality, Fortin operators, and a posteriori estimators.