A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909704427405312 |
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| author | Harmon, Jake Kronbichler, Martin Maier, Matthias Tovar, Eric |
| author_facet | Harmon, Jake Kronbichler, Martin Maier, Matthias Tovar, Eric |
| contents | We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with suitable refinement indicators, the proposed scheme enables a provably IDP adaptive numerical method for hyperbolic systems where preservation of physical properties is essential. In addition to proofs of these characteristics, we supply a detailed construction of the method in the context of a high-performance finite element code. To illustrate our proposed scheme, we study a suite of computationally challenging benchmark problems, demonstrating enhanced accuracy and efficiency properties while entirely avoiding \emph{ad hoc} corrections to preserve physical invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement Harmon, Jake Kronbichler, Martin Maier, Matthias Tovar, Eric Numerical Analysis 65M60, 65M12, 35L50, 35L65, 76M10 We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with suitable refinement indicators, the proposed scheme enables a provably IDP adaptive numerical method for hyperbolic systems where preservation of physical properties is essential. In addition to proofs of these characteristics, we supply a detailed construction of the method in the context of a high-performance finite element code. To illustrate our proposed scheme, we study a suite of computationally challenging benchmark problems, demonstrating enhanced accuracy and efficiency properties while entirely avoiding \emph{ad hoc} corrections to preserve physical invariants. |
| title | A conservative invariant-domain preserving projection technique for hyperbolic systems under adaptive mesh refinement |
| topic | Numerical Analysis 65M60, 65M12, 35L50, 35L65, 76M10 |
| url | https://arxiv.org/abs/2507.18717 |