In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by F\"uhrer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated. The proof of the latter easily extends to a large class of least-squares formulations.

翻译：在[2019]年,F\"元首和Karkulik"所著的抛物线方程式的空间-时间最小方块的限定要素,ArXiv:1911.01.942, 证明了对热方程式的空间-时间第一正方块系统最低方块的精心配置。在目前的工作中,这一结果被普遍推广到一般的第二等抛物线PDE,可能具有无血蛋白的边界条件,以及由最小方块估量器驱动的标准适应性有限要素方法的简单趋同。后者的证据很容易推广到大类最小方块的配方。