A Residual Based A Posteriori Error Estimators for AFC Schemes for Convection-Diffusion Equations

Abhinav Jha

In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general choice of the limiter which defines the nonlinear stabilization term. In the diffusion-dominated regime, the estimator has the same convergence properties as the true error. A second approach is discussed, where the upper bound is derived in a posteriori way using the SUPG estimator proposed in John & Novo, (2013). Numerical examples study the effectivity index and the adaptive grid refinement for two limiters.

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