A discontinuous Galerkin method for elliptic-hyperbolic equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908947522256896 |
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| author | Perinati, Chiara Imbert-Gérard, Lise-Marie Moiola, Andrea Stocker, Paul |
| author_facet | Perinati, Chiara Imbert-Gérard, Lise-Marie Moiola, Andrea Stocker, Paul |
| contents | We present and analyze a discontinuous Galerkin method for the numerical solution of a class of second-order linear mixed-type partial differential equations, i.e. equations that change their nature from elliptic to hyperbolic through the computational domain. Well-posedness of the discrete problem is established via coercivity in an energy norm, achieved through the Morawetz multiplier technique. We derive $hp$-a priori error estimates in the energy norm, which we use to prove convergence rates for standard and quasi-Trefftz polynomial spaces. Numerical experiments validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A discontinuous Galerkin method for elliptic-hyperbolic equations Perinati, Chiara Imbert-Gérard, Lise-Marie Moiola, Andrea Stocker, Paul Numerical Analysis 65N15, 65N30, 35M12, 41A10, 41A25 We present and analyze a discontinuous Galerkin method for the numerical solution of a class of second-order linear mixed-type partial differential equations, i.e. equations that change their nature from elliptic to hyperbolic through the computational domain. Well-posedness of the discrete problem is established via coercivity in an energy norm, achieved through the Morawetz multiplier technique. We derive $hp$-a priori error estimates in the energy norm, which we use to prove convergence rates for standard and quasi-Trefftz polynomial spaces. Numerical experiments validate the theoretical results. |
| title | A discontinuous Galerkin method for elliptic-hyperbolic equations |
| topic | Numerical Analysis 65N15, 65N30, 35M12, 41A10, 41A25 |
| url | https://arxiv.org/abs/2604.06910 |