The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method
We describe how a discontinuous Galerkin finite element method with interior penalty can be used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated. We show that, in order to have an adjoint consistent method and thus obtain...
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| Format: | Report |
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Unspecified
2004
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| _version_ | 1797050486410444800 |
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| author | Harriman, K Gavaghan, D Suli, E |
| author_facet | Harriman, K Gavaghan, D Suli, E |
| author_sort | Harriman, K |
| collection | OXFORD |
| description | We describe how a discontinuous Galerkin finite element method with interior penalty can be used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated. We show that, in order to have an adjoint consistent method and thus obtain optimal rates of convergence of the functional, a symmetric interior penalty Galerkin method must be used and, when the functional depends on the derivative of the solution of the PDE, an equivalent formulation of the functional must be used. |
| first_indexed | 2024-03-06T18:05:52Z |
| format | Report |
| id | oxford-uuid:01694f59-b28c-4ba4-87ae-0047cdae9b77 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:05:52Z |
| publishDate | 2004 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:01694f59-b28c-4ba4-87ae-0047cdae9b772022-03-26T08:34:46ZThe importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element methodReporthttp://purl.org/coar/resource_type/c_93fcuuid:01694f59-b28c-4ba4-87ae-0047cdae9b77Mathematical Institute - ePrintsUnspecified2004Harriman, KGavaghan, DSuli, EWe describe how a discontinuous Galerkin finite element method with interior penalty can be used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated. We show that, in order to have an adjoint consistent method and thus obtain optimal rates of convergence of the functional, a symmetric interior penalty Galerkin method must be used and, when the functional depends on the derivative of the solution of the PDE, an equivalent formulation of the functional must be used. |
| spellingShingle | Harriman, K Gavaghan, D Suli, E The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title | The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title_full | The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title_fullStr | The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title_full_unstemmed | The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title_short | The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method |
| title_sort | importance of adjoint consistency in the approximation of linear functionals using the discontinuous galerkin finite element method |
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