后向Euler原始DPG方法的分析
Analysis of backward Euler primal DPG methods
摘要：
我们分析了一类抛物型问题的原始DPG格式的向后欧拉时间推进格式。最佳误差估计显示在自然范数和$L^2$范数的字段变量。对于热方程的解决方案，我们的原始DPG制定等于解决方案的标准Galerkin计划，因此，最佳的误差界中找到的文献。然而，在对流和反应项的存在下，后者的身份是无效的，最佳误差界的分析需要诉诸椭圆投影算子。至关重要的是，这些运营商的投影相对于PDE的空间部分，在标准的Galerkin计划，而不是相对于完整的PDE在一个时间步长，如前所述。
英文摘要：
We analyse backward Euler time stepping schemes for the primal DPG formulation of a class of parabolic problems. Optimal error estimates are shown in the natural norm and in the $L^2$ norm of the field variable. For the heat equation the solution of our primal DPG formulation equals the solution of a standard Galerkin scheme and, thus, optimal error bounds are found in the literature. In the presence of advection and reaction terms, however, the latter identity is not valid anymore and the analysis of optimal error bounds requires to resort to elliptic projection operators. It is essential that these operators be projections with respect to the spatial part of the PDE, as in standard Galerkin schemes, and not with respect to the full PDE at a time step, as done previously.
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