A robust goal-oriented estimator based on the construction of equilibrated fluxes for discontinuous Galerkin finite element approximations of convection-diffusion problems
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Bibliographic record
Abstract
We propose an a posteriori error estimator with respect to quantities of interest for dis-continuous Galerkin approximations of convection-diffusion boundary-value problems. The error estimator is based on the construction of equilibrated fluxes in Raviart-Thomas finite element spaces and on the solution of the dual problem. We show that it is asymptotically exact in both the elliptic and hyperbolic regimes if the dual problem is approximated by a discontinuous Galerkin method of order one greater than that of the primal problem. We show in this case that the effectivity index behaves as (1+Pe 1/2)o(h), where Pe is the Péclet number and h the mesh diameter. It follows that the quality of the effectivity index may deteriorate for large values of Pe, but we put in evidence that it suffices to increase the approximation order of the dual problem to keep the effectivity index close to unity even on coarse meshes. Two-dimensional numerical examples demonstrate the robustness of the error estimator in both the diffusion and advection regimes.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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