A class of Discontinuous Galerkin methods for nonlinear variational problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915136298549248 |
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| author | Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambos Vikelis, Andreas |
| author_facet | Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambos Vikelis, Andreas |
| contents | In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous minimisation problem. Using $Γ$-convergence arguments we show that the discrete minimisers converge to the unique minimiser of the continuous problem as the mesh parameter tends to zero, under the additional contribution of appropriately defined penalty terms at the level of the discrete energies. We finally substantiate the feasibility of our methods by numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12891 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A class of Discontinuous Galerkin methods for nonlinear variational problems Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambos Vikelis, Andreas Numerical Analysis (Primary) 65N30, 49J45 In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous minimisation problem. Using $Γ$-convergence arguments we show that the discrete minimisers converge to the unique minimiser of the continuous problem as the mesh parameter tends to zero, under the additional contribution of appropriately defined penalty terms at the level of the discrete energies. We finally substantiate the feasibility of our methods by numerical examples. |
| title | A class of Discontinuous Galerkin methods for nonlinear variational problems |
| topic | Numerical Analysis (Primary) 65N30, 49J45 |
| url | https://arxiv.org/abs/2308.12891 |