Error estimates for completely discrete FEM in energy-type and weaker norms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915768977850368 |
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| author | Angermann, Lutz Knabner, Peter Rupp, Andreas |
| author_facet | Angermann, Lutz Knabner, Peter Rupp, Andreas |
| contents | The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity nor consistency properties are assumed, the method is called completely discrete. We investigate two different stabilized discretizations and obtain stability and optimal error estimates in energy-type norms and, by generalizing the Aubin-Nitsche technique, optimal error estimates in weaker norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06860 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Error estimates for completely discrete FEM in energy-type and weaker norms Angermann, Lutz Knabner, Peter Rupp, Andreas Numerical Analysis 65N12, 65N30, 46B10 The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity nor consistency properties are assumed, the method is called completely discrete. We investigate two different stabilized discretizations and obtain stability and optimal error estimates in energy-type norms and, by generalizing the Aubin-Nitsche technique, optimal error estimates in weaker norms. |
| title | Error estimates for completely discrete FEM in energy-type and weaker norms |
| topic | Numerical Analysis 65N12, 65N30, 46B10 |
| url | https://arxiv.org/abs/2301.06860 |