Applications of a space-time FOSLS formulation for parabolic PDEs

TL;DR

This paper demonstrates that a space-time FOSLS formulation for parabolic PDEs can efficiently handle parameter-dependent, optimal control, and time-dependent domain problems, extending its applicability beyond the heat equation.

Contribution

It generalizes the space-time FOSLS approach to a broader class of second-order parabolic PDEs and showcases its effectiveness for complex, real-world problems.

Findings

Efficient solution of parameter-dependent parabolic problems

Application to optimal control scenarios

Handling of problems on time-dependent spatial domains

Abstract

In this work, we show that the space-time first-order system least-squares (FOSLS) formulation [F\"uhrer, Karkulik, Comput. Math. Appl. 92 (2021)] for the heat equation and its recent generalization [Gantner, Stevenson, ESAIM Math. Model. Numer. Anal. 55 (2021)] to arbitrary second-order parabolic PDEs can be used to efficiently solve parameter-dependent problems, optimal control problems, and problems on time-dependent spatial domains.