Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912738532392960 |
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| author | Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul Voulis, Igor |
| author_facet | Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul Voulis, Igor |
| contents | This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous Galerkin method, for a wide range of second-order scalar elliptic partial differential equations and a scalar reaction-advection problem. We also analyze quasi-Trefftz methods with our framework, presenting the first optimal error bounds in weaker norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul Voulis, Igor Numerical Analysis This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous Galerkin method, for a wide range of second-order scalar elliptic partial differential equations and a scalar reaction-advection problem. We also analyze quasi-Trefftz methods with our framework, presenting the first optimal error bounds in weaker norms. |
| title | Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.00806 |