no. 1
Further results on a space-time FOSLS formulation of parabolic PDEs
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 1, pp. 283-299

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

DOI : 10.1051/m2an/2020084
Classification : 35K20, 65M12, 65M15, 65M60
Keywords: Parabolic PDEs, boundary conditions, space-time FOSLS, convergence of adaptive algorithm 
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Gantner, Gregor; Stevenson, Rob. Further results on a space-time FOSLS formulation of parabolic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 1, pp. 283-299. doi: 10.1051/m2an/2020084

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