Trefftz Discontinuous Galerkin discretization for the Stokes problem
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913198409515008 |
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| author | Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul |
| author_facet | Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul |
| contents | We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwise within each element and yield element-wise divergence-free solutions. Compared to standard DG methods, a strong reduction of the degrees of freedom is achieved, especially for higher order polynomial degrees. In addition, in contrast to many other Trefftz-DG methods, our approach allows to easily incorporate inhomogeneous right hand sides (driving forces) by using the concept of the embedded Trefftz-DG method. On top of a detailed a priori error analysis, we further compare our approach to standard discontinuous Galerkin Stokes discretizations and present numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_14600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trefftz Discontinuous Galerkin discretization for the Stokes problem Lederer, Philip L. Lehrenfeld, Christoph Stocker, Paul Numerical Analysis 76D07, 76M10, 65N12, 65N22, 65N30 We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwise within each element and yield element-wise divergence-free solutions. Compared to standard DG methods, a strong reduction of the degrees of freedom is achieved, especially for higher order polynomial degrees. In addition, in contrast to many other Trefftz-DG methods, our approach allows to easily incorporate inhomogeneous right hand sides (driving forces) by using the concept of the embedded Trefftz-DG method. On top of a detailed a priori error analysis, we further compare our approach to standard discontinuous Galerkin Stokes discretizations and present numerical examples. |
| title | Trefftz Discontinuous Galerkin discretization for the Stokes problem |
| topic | Numerical Analysis 76D07, 76M10, 65N12, 65N22, 65N30 |
| url | https://arxiv.org/abs/2306.14600 |