Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915383505584128 |
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| author | Cao, Shuhao Chen, Long Lee, Seulip |
| author_facet | Cao, Shuhao Chen, Long Lee, Seulip |
| contents | This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an $M$-matrix) on Voronoi polygonal meshes, provided their duals are Delaunay triangulations with acute angles. Furthermore, the study outlines a comprehensive framework for EAVE methodologies, introducing another variant that integrates with the stiffness matrix derived from the lowest-order virtual element method for the Poisson equation. Numerical experiments confirm the theoretical advantages of the monotonicity property and demonstrate an optimal convergence rate across various mesh configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems Cao, Shuhao Chen, Long Lee, Seulip Numerical Analysis 65N30, 65N12 This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an $M$-matrix) on Voronoi polygonal meshes, provided their duals are Delaunay triangulations with acute angles. Furthermore, the study outlines a comprehensive framework for EAVE methodologies, introducing another variant that integrates with the stiffness matrix derived from the lowest-order virtual element method for the Poisson equation. Numerical experiments confirm the theoretical advantages of the monotonicity property and demonstrate an optimal convergence rate across various mesh configurations. |
| title | Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems |
| topic | Numerical Analysis 65N30, 65N12 |
| url | https://arxiv.org/abs/2402.13347 |