Minimal residual discretization of a class of fully nonlinear elliptic PDE
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912460814942208 |
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| author | Gallistl, Dietmar Tran, Ngoc Tien |
| author_facet | Gallistl, Dietmar Tran, Ngoc Tien |
| contents | This work introduces finite element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov--Bakelman--Pucci estimate. Under rather general structural assumptions on the operator, convergence of $C^1$ conforming and discontinuous Galerkin methods is proven in the $L^\infty$ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal residual discretization of a class of fully nonlinear elliptic PDE Gallistl, Dietmar Tran, Ngoc Tien Numerical Analysis This work introduces finite element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov--Bakelman--Pucci estimate. Under rather general structural assumptions on the operator, convergence of $C^1$ conforming and discontinuous Galerkin methods is proven in the $L^\infty$ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided. |
| title | Minimal residual discretization of a class of fully nonlinear elliptic PDE |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.07568 |