A unified framework for the analysis, numerical approximation and model reduction of linear operator equations, Part I: Well-posedness in space and time
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908481335853056 |
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| author | Feuerle, Moritz Löscher, Richard Steinbach, Olaf Urban, Karsten |
| author_facet | Feuerle, Moritz Löscher, Richard Steinbach, Olaf Urban, Karsten |
| contents | We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak variational formulations as well as novel space-time variational forms of the hyperbolic wave equation. The main concept is completion and extension of operators starting from the strong form of the problem.
This paper lays the theoretical foundation for a unified approach towards numerical approximation methods and also model reduction of parameterized linear operator equations which will be the subject of the following parts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unified framework for the analysis, numerical approximation and model reduction of linear operator equations, Part I: Well-posedness in space and time Feuerle, Moritz Löscher, Richard Steinbach, Olaf Urban, Karsten Numerical Analysis 35R20, 35A15, 65N12 We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak variational formulations as well as novel space-time variational forms of the hyperbolic wave equation. The main concept is completion and extension of operators starting from the strong form of the problem. This paper lays the theoretical foundation for a unified approach towards numerical approximation methods and also model reduction of parameterized linear operator equations which will be the subject of the following parts. |
| title | A unified framework for the analysis, numerical approximation and model reduction of linear operator equations, Part I: Well-posedness in space and time |
| topic | Numerical Analysis 35R20, 35A15, 65N12 |
| url | https://arxiv.org/abs/2508.05407 |