Convergence properties of the Lagrange-Galerkin method with and without exact integration
The properties of the Lagrange-Galerkin finite element method are investigated for advection and advection-diffusion problems. In one dimension, we investigate convergence rates of the method for a variety of initial data of differing smoothness on uniform and non-uniform meshes, with linear and qua...
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| Format: | Report |
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Unspecified
1987
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| _version_ | 1797059450504216576 |
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| author | Jack, R |
| author_facet | Jack, R |
| author_sort | Jack, R |
| collection | OXFORD |
| description | The properties of the Lagrange-Galerkin finite element method are investigated for advection and advection-diffusion problems. In one dimension, we investigate convergence rates of the method for a variety of initial data of differing smoothness on uniform and non-uniform meshes, with linear and quadratic elements. In two dimensions, we carry out numerical experiments on two test problems. The first is the advection problem. The properties of area-weighting and the exactly integrated scheme are compared and a refinement of area-weighting called compound area-weighting introduced to improve accuracy. Comparison is also made between the performance of bilinear and biquadratic elements. The other test case is an advection diffusion problem - scalar transport in a reversed flow field. |
| first_indexed | 2024-03-06T20:04:26Z |
| format | Report |
| id | oxford-uuid:28756e1d-c804-4c32-9001-3bd1e4162774 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:04:26Z |
| publishDate | 1987 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:28756e1d-c804-4c32-9001-3bd1e41627742022-03-26T12:12:52ZConvergence properties of the Lagrange-Galerkin method with and without exact integrationReporthttp://purl.org/coar/resource_type/c_93fcuuid:28756e1d-c804-4c32-9001-3bd1e4162774Mathematical Institute - ePrintsUnspecified1987Jack, RThe properties of the Lagrange-Galerkin finite element method are investigated for advection and advection-diffusion problems. In one dimension, we investigate convergence rates of the method for a variety of initial data of differing smoothness on uniform and non-uniform meshes, with linear and quadratic elements. In two dimensions, we carry out numerical experiments on two test problems. The first is the advection problem. The properties of area-weighting and the exactly integrated scheme are compared and a refinement of area-weighting called compound area-weighting introduced to improve accuracy. Comparison is also made between the performance of bilinear and biquadratic elements. The other test case is an advection diffusion problem - scalar transport in a reversed flow field. |
| spellingShingle | Jack, R Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title | Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title_full | Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title_fullStr | Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title_full_unstemmed | Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title_short | Convergence properties of the Lagrange-Galerkin method with and without exact integration |
| title_sort | convergence properties of the lagrange galerkin method with and without exact integration |
| work_keys_str_mv | AT jackr convergencepropertiesofthelagrangegalerkinmethodwithandwithoutexactintegration |