Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation
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Date
2021
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Abstract
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. (C) 2020 Elsevier Ltd. All rights reserved.
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DPG method, Ultraweak formulation, Cordes coefficients