Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916334360592384 |
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| author | Erath, Christoph Mascotto, Lorenzo Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander |
| author_facet | Erath, Christoph Mascotto, Lorenzo Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander |
| contents | We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the $h$- and $p$-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_06173 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation Erath, Christoph Mascotto, Lorenzo Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander Numerical Analysis 65N38, 65N12, 65N15, 35J05, 65R20 We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the $h$- and $p$-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces. |
| title | Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation |
| topic | Numerical Analysis 65N38, 65N12, 65N15, 35J05, 65R20 |
| url | https://arxiv.org/abs/2105.06173 |