A robust a-posteriori error estimator for discontinuous Galerkin methods for convection-diffusion equations. (English) Zbl 1169.65108
The authors propose and analyze a robust a-posteriori error estimator for discontinuous Galerkin discretizations of stationary convection-diffusion problems. They utilize the upwind discretization of the transport terms and the classical interior penalty method for the diffusive terms. The estimator yields global upper and lower bounds of the error measured in terms of the energy norm and a semi-norm associated with the convective term in the equation. The ratio of the upper and lower bounds is independent of the magnitude of the Péclet number of the problem, and hence the estimator is fully robust for convection-dominated problems. The error measure used in the paper includes a non-local norm. Numerical examples indicate that this error contribution is smaller than the energy error and of high order once the mesh is sufficiently refined.
Reviewer: Adrian Carabineanu (Bucureşti)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
robust a posteriori error estimator; stationary convection-diffusion equations; discontinuous Galerkin methods; upwind discretization; interior penalty method; numerical examplesSoftware:
deal.iiReferences:
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