Further results on a space-time FOSLS formulation of parabolic PDEs

In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Fuhrer& 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.