hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems
We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first--order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our...
| Principais autores: | , |
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| Formato: | Report |
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Unspecified
2001
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| Resumo: | We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first--order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree-variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments. |
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