A review of discontinuous Galerkin time-stepping methods for wave propagation problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918014911250432 |
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| author | Antonietti, Paola F. Artoni, Alberto Ciaramella, Gabriele Mazzieri, Ilario |
| author_facet | Antonietti, Paola F. Artoni, Alberto Ciaramella, Gabriele Mazzieri, Ilario |
| contents | This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave propagation problems. Two formulations, tailored for second- and first-order systems of ordinary differential equations, are discussed within a generalized framework, assessing their stability, accuracy, and computational efficiency. Theoretical results are supported by various illustrative examples that validate the findings, enhancing the understanding and applicability of these methods in practical scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A review of discontinuous Galerkin time-stepping methods for wave propagation problems Antonietti, Paola F. Artoni, Alberto Ciaramella, Gabriele Mazzieri, Ilario Numerical Analysis This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave propagation problems. Two formulations, tailored for second- and first-order systems of ordinary differential equations, are discussed within a generalized framework, assessing their stability, accuracy, and computational efficiency. Theoretical results are supported by various illustrative examples that validate the findings, enhancing the understanding and applicability of these methods in practical scenarios. |
| title | A review of discontinuous Galerkin time-stepping methods for wave propagation problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.05978 |