论文标题
对流扩散方程DPG离散化的强大的准最佳测试规范
A robust quasi-optimal test norm for a DPG discretization of the convection-diffusion equation
论文作者
论文摘要
在这项工作中，我们为对流扩散方程的超促进配方的不连续的彼得 - 盖尔金（DPG）离散化了新的准最佳测试规范。从理论上讲，我们证明了所提出的测试规范会导致目标标准与测试规范引起的能量规范之间的界限，这些范围相对于解决方案和梯度成分的扩散参数稳健，并且在痕量成分中具有良好的量表。我们以数值实验确认我们的理论结果。
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 are robust with respect to the diffusion parameter in the solution and gradient components and have favorable scalings in the trace components. We conclude with numerical experiments to confirm our theoretical results.
