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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2004
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0403517 |
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| _version_ | 1866909853456269312 |
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| author | Bornemann, Folkmar Rasch, Christian |
| author_facet | Bornemann, Folkmar Rasch, Christian |
| contents | We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0403517 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle Bornemann, Folkmar Rasch, Christian Numerical Analysis 65N30 (Primary) 35F30, 49L20, 49M05, 65N12, 65N22 (Secondary) We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show. |
| title | Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle |
| topic | Numerical Analysis 65N30 (Primary) 35F30, 49L20, 49M05, 65N12, 65N22 (Secondary) |
| url | https://arxiv.org/abs/math/0403517 |