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

Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation