On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids
In this paper we propose the addition of an artificial diffusion model to the Lagrange-Galerkin finite element method, which is dependent on both the mesh function $h$ and the numerical solution $u_{h}$. The purpose of this additional term is to produce smooth approximations to sharp features of the...
| Main Authors: | , |
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| Format: | Report |
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Unspecified
1996
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| _version_ | 1797097474862612480 |
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| author | Houston, P Suli, E |
| author_facet | Houston, P Suli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | In this paper we propose the addition of an artificial diffusion model to the Lagrange-Galerkin finite element method, which is dependent on both the mesh function $h$ and the numerical solution $u_{h}$. The purpose of this additional term is to produce smooth approximations to sharp features of the solution, such as internal and boundary layers. Moreover, the added diffusion will help to stabilise the numerical scheme. Further, we extend the a posteriori error analysis presented in Technical Report NA-95/24 to include this artificial diffusion model. Based on this a posteriori estimate, we design an adaptive algorithm to ensure global control of the error in the $L^{2}(L^{2})$ norm with respect to a pre-determined tolerance. The performance of this numerical algorithm is demonstrated by some numerical experiments. |
| first_indexed | 2024-03-07T04:56:02Z |
| format | Report |
| id | oxford-uuid:d6a2f2e8-e153-4c7b-8f3a-91e42920adfc |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:56:02Z |
| publishDate | 1996 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:d6a2f2e8-e153-4c7b-8f3a-91e42920adfc2022-03-27T08:34:57ZOn the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular gridsReporthttp://purl.org/coar/resource_type/c_93fcuuid:d6a2f2e8-e153-4c7b-8f3a-91e42920adfcMathematical Institute - ePrintsUnspecified1996Houston, PSuli, EIn this paper we propose the addition of an artificial diffusion model to the Lagrange-Galerkin finite element method, which is dependent on both the mesh function $h$ and the numerical solution $u_{h}$. The purpose of this additional term is to produce smooth approximations to sharp features of the solution, such as internal and boundary layers. Moreover, the added diffusion will help to stabilise the numerical scheme. Further, we extend the a posteriori error analysis presented in Technical Report NA-95/24 to include this artificial diffusion model. Based on this a posteriori estimate, we design an adaptive algorithm to ensure global control of the error in the $L^{2}(L^{2})$ norm with respect to a pre-determined tolerance. The performance of this numerical algorithm is demonstrated by some numerical experiments. |
| spellingShingle | Houston, P Suli, E On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title | On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title_full | On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title_fullStr | On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title_full_unstemmed | On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title_short | On the design of an artificial diffusion model for the Lagrange-Galerkin method on unstructured triangular grids |
| title_sort | on the design of an artificial diffusion model for the lagrange galerkin method on unstructured triangular grids |
| work_keys_str_mv | AT houstonp onthedesignofanartificialdiffusionmodelforthelagrangegalerkinmethodonunstructuredtriangulargrids AT sulie onthedesignofanartificialdiffusionmodelforthelagrangegalerkinmethodonunstructuredtriangulargrids |