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.

中文翻译：

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不发散形式的线性PDE的超弱公式化和DPG近似

我们开发和分析系数满足Cordes条件的非散度线性PDE的超弱公式。基于超弱公式，我们提出了不连续的Petrov-Galerkin（DPG）方法。我们调查Fortin算子的完全离散方案，并为所考虑的方法提供后验估计。在均匀和自适应网格细化的情况下，进行了数值实验。