| Issue |
ESAIM: M2AN
Volume 55, Number 1, January-February 2021
|
|
|---|---|---|
| Page(s) | 283 - 299 | |
| DOI | https://doi.org/10.1051/m2an/2020084 | |
| Published online | 18 February 2021 | |
Further results on a space-time FOSLS formulation of parabolic PDEs
Korteweg-de Vries (KdV) Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE, Amsterdam, The Netherlands
* Corresponding author: g.gantner@uva.nl
Received:
20
May
2020
Accepted:
8
December
2020
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.
Mathematics Subject Classification: 35K20 / 65M12 / 65M15 / 65M60
Key words: Parabolic PDEs / boundary conditions / space-time FOSLS / convergence of adaptive algorithm
© EDP Sciences, SMAI 2021
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