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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2601.21736 |
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| _version_ | 1866914291168313344 |
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| author | Hinze, Michael Kahle, Christian Stahl, Michael |
| author_facet | Hinze, Michael Kahle, Christian Stahl, Michael |
| contents | In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze, Kahle, Stahl, A least-squares space-time approach for parabolic equations, 2023, arXiv:2305.03402] that assumes only minimal regularity. We extend this approach to the parameter-dependent case. The corresponding variational formulation then is based on a parameter-dependent, symmetric, uniformly coercive, and continuous bilinear form. We apply the reduced basis method to this formulation, following the well-developed techniques for parameterized coercive problems, as seen e.g. in reduced basis methods for parameterized elliptic PDEs. We present an offline-online decomposition and provide certification with absolute and relative error bounds. The performance of the method is demonstrated using selected numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A reduced basis method for parabolic PDEs based on a space-time least squares formulation Hinze, Michael Kahle, Christian Stahl, Michael Numerical Analysis In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze, Kahle, Stahl, A least-squares space-time approach for parabolic equations, 2023, arXiv:2305.03402] that assumes only minimal regularity. We extend this approach to the parameter-dependent case. The corresponding variational formulation then is based on a parameter-dependent, symmetric, uniformly coercive, and continuous bilinear form. We apply the reduced basis method to this formulation, following the well-developed techniques for parameterized coercive problems, as seen e.g. in reduced basis methods for parameterized elliptic PDEs. We present an offline-online decomposition and provide certification with absolute and relative error bounds. The performance of the method is demonstrated using selected numerical examples. |
| title | A reduced basis method for parabolic PDEs based on a space-time least squares formulation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.21736 |