A least squares space-time approach for parabolic equations
- We propose a least squares formulation for abstract parabolic equations in the natural L2(0,T;V⋆)×Hnorm which only relies on natural regularity assumptions on the data of the problem. The resulting bilinear form then is symmetric, coercive, and continuous and contains the V⋆-norm. We propose a solution approach that uses a conforming Galerkin discretization of an equivalent saddle point problem to circumvent the evaluation of V⋆-norms. We prove strong convergence of discrete solutions towards continuous solutions and provide a preconditioner for efficient numerical solution of the discrete saddle point problem. We illustrate our analytical findings by selected numerical experiments.
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| Author: | Michael HinzeORCID, Christian KahleORCID, Michael StahlORCID |
|---|---|
| URN: | urn:nbn:de:hbz:kob7-27286 |
| DOI: | https://doi.org/10.1007/s10444-026-10345-0 |
| ISSN: | 1019-7168 |
| ISSN: | 1572-9044 |
| Parent Title (English): | Advances in Computational Mathematics |
| Publisher: | Springer |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2026/08/20 |
| Date of first Publication: | 2026/08/20 |
| Publishing Institution: | Universität Koblenz, Universitätsbibliothek |
| Release Date: | 2026/08/21 |
| Tag: | Least squares formulation; Saddle point problem; Space-time finite elements |
| Volume: | 52 |
| Issue: | 5 |
| Article Number: | 70 |
| Page Number: | 24 |
| Licence (German): |  CC BY - Namensnennung 4.0 International |
