Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Führer, Thomas Gantner, Gregor |
| author_facet | Führer, Thomas Gantner, Gregor |
| contents | We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, which are satisfied if the spatial domain is convex and the heat source and initial datum are sufficiently smooth, we prove that the $L^2$ error of approximations of the scalar field variable converges at a higher rate than the overall error. Furthermore, a higher-order conservation property is shown. In addition, we discuss quasi-optimality in weaker norms. Numerical experiments confirm our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs Führer, Thomas Gantner, Gregor Numerical Analysis 35K20, 65M12, 65M60 We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, which are satisfied if the spatial domain is convex and the heat source and initial datum are sufficiently smooth, we prove that the $L^2$ error of approximations of the scalar field variable converges at a higher rate than the overall error. Furthermore, a higher-order conservation property is shown. In addition, we discuss quasi-optimality in weaker norms. Numerical experiments confirm our theoretical findings. |
| title | Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs |
| topic | Numerical Analysis 35K20, 65M12, 65M60 |
| url | https://arxiv.org/abs/2412.04651 |