A Hybridizable Discontinuous Galerkin Method for the non--local Camassa--Holm--Kadomtsev--Petviashvili equation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914266134609920 |
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| author | Dwivedi, Mukul Gutendorf, Ruben Rupp, Andreas |
| author_facet | Dwivedi, Mukul Gutendorf, Ruben Rupp, Andreas |
| contents | This paper develops a hybridizable discontinuous Galerkin method for the two-dimensional Camassa--Holm--Kadomtsev--Petviashvili equation. The method employs Cartesian meshes with tensor-product polynomial spaces, enabling separate treatment of \(x\) and \(y\) derivatives. The non-local operator \(\partial_{x}^{-1}u_{y}\) is localized through an auxiliary variable \(v\) satisfying \(v_x = u_y\), allowing efficient element-by-element computations. We prove energy stability of the semi-discrete scheme and derive \(\mathcal{O}(h^{k+1/2})\) convergence in space. Numerical experiments validate the theoretical results and demonstrate the method's capability to accurately resolve smooth solutions and peaked solitary waves (peakons). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13800 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Hybridizable Discontinuous Galerkin Method for the non--local Camassa--Holm--Kadomtsev--Petviashvili equation Dwivedi, Mukul Gutendorf, Ruben Rupp, Andreas Numerical Analysis This paper develops a hybridizable discontinuous Galerkin method for the two-dimensional Camassa--Holm--Kadomtsev--Petviashvili equation. The method employs Cartesian meshes with tensor-product polynomial spaces, enabling separate treatment of \(x\) and \(y\) derivatives. The non-local operator \(\partial_{x}^{-1}u_{y}\) is localized through an auxiliary variable \(v\) satisfying \(v_x = u_y\), allowing efficient element-by-element computations. We prove energy stability of the semi-discrete scheme and derive \(\mathcal{O}(h^{k+1/2})\) convergence in space. Numerical experiments validate the theoretical results and demonstrate the method's capability to accurately resolve smooth solutions and peaked solitary waves (peakons). |
| title | A Hybridizable Discontinuous Galerkin Method for the non--local Camassa--Holm--Kadomtsev--Petviashvili equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.13800 |