Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms
The effects of dual consistency on discontinuous Galerkin discretizations of solution and solution gradient dependent source terms are examined. Two common discretizations are analyzed: the standard weighting technique for source terms and the mixed formulation. It is shown that if the source term d...
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| Format: | Article |
| Language: | English |
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Society for Industrial and Applied Mathematics,
2010-03-08T21:09:36Z.
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| Online Access: | Get fulltext |
| Summary: | The effects of dual consistency on discontinuous Galerkin discretizations of solution and solution gradient dependent source terms are examined. Two common discretizations are analyzed: the standard weighting technique for source terms and the mixed formulation. It is shown that if the source term depends on the first derivative of the solution, the standard weighting technique leads to a dual inconsistent scheme. A straightforward procedure for correcting this dual inconsistency and arriving at a dual consistent discretization is demonstrated. The mixed formulation, where the solution gradient in the source term is replaced by an additional variable that is solved for simultaneously with the state, leads to an asymptotically dual consistent discretization. Numerical results for a one-dimensional test problem confirm that the dual consistent and asymptotically dual consistent schemes achieve higher asymptotic convergence rates with grid refinement than a similar dual inconsistent scheme for both the primal and adjoint solutions as well as a simple functional output. Boeing Company U. S. Air Force Research Laboratory (USAF-3306-03-SC-0001) |
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