Applications of a space-time FOSLS formulation for parabolic PDEs

In this work, we show that the space-time first-order system least-squares formulation (Führer, T. & Karkulik, M. (2021) Space-time least-squares finite elements for parabolic equations. Comput. Math. Appl. 92, 27-36) for the heat equation and its recent generalization (Gantner, G. & Stevenson, R. (2021) Further results on a space-time FOSLS formulation of parabolic PDEs. ESAIM Math. Model. Numer. Anal. 55, 283-299) to arbitrary second-order parabolic partial differential equations can be used to efficiently solve parameter-dependent problems, optimal control problems and problems on time-dependent spatial domains.