Semi-discrete Active Flux as a Petrov-Galerkin method
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913999182888960 |
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| author | Barsukow, Wasilij |
| author_facet | Barsukow, Wasilij |
| contents | Active Flux (AF) is a recent numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus combines ideas from Finite Volume/Discontinuous Galerkin (DG) methods with a continuous approximation common in continuous Finite Element (CG) methods. This work shows that the semi-discrete Active Flux method on Cartesian meshes can be obtained from a variational formulation through a particular choice of (biorthogonal) test functions. These latter being discontinuous, the new formulation emphasizes the intermediate nature of AF between DG and CG. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-discrete Active Flux as a Petrov-Galerkin method Barsukow, Wasilij Numerical Analysis Active Flux (AF) is a recent numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus combines ideas from Finite Volume/Discontinuous Galerkin (DG) methods with a continuous approximation common in continuous Finite Element (CG) methods. This work shows that the semi-discrete Active Flux method on Cartesian meshes can be obtained from a variational formulation through a particular choice of (biorthogonal) test functions. These latter being discontinuous, the new formulation emphasizes the intermediate nature of AF between DG and CG. |
| title | Semi-discrete Active Flux as a Petrov-Galerkin method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.15017 |