In this work, we propose a new quasi-optimal test norm for a discontinuous Petrov-Galerkin (DPG) discretization of the ultra-weak formulation of the convection-diffusion equation. We prove theoretically that the proposed test norm leads to bounds between the target norm and the energy norm induced by the test norm which have favorable scalings with respect to the diffusion parameter when compared with existing results for other test norms from the literature. We conclude with numerical experiments to confirm our theoretical results.

中文翻译：

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对流扩散方程的DPG离散化的拟最佳测试范数

在这项工作中，我们提出了对流扩散方程的超弱公式的不连续Petrov-Galerkin（DPG）离散化的新的拟最佳测试范数。我们从理论上证明，与文献中其他测试规范的现有结果相比，拟议的测试规范导致目标规范和由测试规范引发的能量规范之间的界限，这些界限对扩散参数具有良好的缩放比例。我们通过数值实验得出结论，以证实我们的理论结果。