High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations
© 2017 Society for Industrial and Applied Mathematics. We derive a high order globally continuous and locally conservative flux field and a high order finite-volume-like solution from the continuous Galerkin (CG) finite element solution. The main idea is to postprocess the CG solution by solving a s...
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| Format: | Journal Article |
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Society for Industrial and Applied Mathematics
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/65703 |
| _version_ | 1848761185583759360 |
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| author | Zou, Q. Guo, L. Deng, Quanling |
| author_facet | Zou, Q. Guo, L. Deng, Quanling |
| author_sort | Zou, Q. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Society for Industrial and Applied Mathematics. We derive a high order globally continuous and locally conservative flux field and a high order finite-volume-like solution from the continuous Galerkin (CG) finite element solution. The main idea is to postprocess the CG solution by solving a small linear algebraic system on each element of the underlying mesh. Both the postprocessed flux field and the finite-volume-like solution satisfy the conservation law on each control volume of the dual mesh. Moreover, both the postprocessed flux field and the gradient of finite-volume-like solution converge to the exact flux with optimal convergence rates. Our theoretical findings are validated by our numerical experiments. |
| first_indexed | 2025-11-14T10:27:39Z |
| format | Journal Article |
| id | curtin-20.500.11937-65703 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:27:39Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-657032018-02-19T08:06:06Z High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations Zou, Q. Guo, L. Deng, Quanling © 2017 Society for Industrial and Applied Mathematics. We derive a high order globally continuous and locally conservative flux field and a high order finite-volume-like solution from the continuous Galerkin (CG) finite element solution. The main idea is to postprocess the CG solution by solving a small linear algebraic system on each element of the underlying mesh. Both the postprocessed flux field and the finite-volume-like solution satisfy the conservation law on each control volume of the dual mesh. Moreover, both the postprocessed flux field and the gradient of finite-volume-like solution converge to the exact flux with optimal convergence rates. Our theoretical findings are validated by our numerical experiments. 2017 Journal Article http://hdl.handle.net/20.500.11937/65703 10.1137/16M1066567 Society for Industrial and Applied Mathematics restricted |
| spellingShingle | Zou, Q. Guo, L. Deng, Quanling High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title | High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title_full | High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title_fullStr | High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title_full_unstemmed | High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title_short | High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| title_sort | high order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations |
| url | http://hdl.handle.net/20.500.11937/65703 |