标题： Aubin--Nitsche型估计用于抛物PDE的空间时间FOSLS 显示英文标题

标题： Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs

摘要： 我们为最近提出的热方程的一阶系统最小二乘有限元方法（FOSLS）开发了Aubin--Nitsche型估计。 在某些假设下，这些假设在空间域是凸的且热源和初始数据足够光滑时成立，我们证明了标量场变量近似解的$L^2$误差比整体误差收敛得更快。 此外，展示了更高阶的守恒性质。 另外，我们讨论了在更弱范数下的准最优性。 数值实验验证了我们的理论结果。 显示英文摘要

摘要： We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, which are satisfied if the spatial domain is convex and the heat source and initial datum are sufficiently smooth, we prove that the $L^2$ error of approximations of the scalar field variable converges at a higher rate than the overall error. Furthermore, a higher-order conservation property is shown. In addition, we discuss quasi-optimality in weaker norms. Numerical experiments confirm our theoretical findings.