Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation

08/23/2019

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by   Thomas Führer, et al.

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We develop and analyze an ultraweak formulation of linear PDEs in nondivergence form where the coefficients satisfy the Cordes condition. Based on the ultraweak formulation we propose discontinuous Petrov--Galerkin (DPG) methods. We investigate Fortin operators for the fully discrete schemes and provide a posteriori estimators for the methods under consideration. Numerical experiments are presented in the case of uniform and adaptive mesh-refinement.