A Residual Based A Posteriori Error Estimators for AFC Schemes for Convection-Diffusion Equations
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911755378098176 |
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| author | Jha, Abhinav |
| author_facet | Jha, Abhinav |
| contents | 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 Streamline Upwind Petrov Galerkin (SUPG) estimator proposed in \cite{JN13}. Numerical examples study the effectivity index and the adaptive grid refinement for two limiters in two dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2005_02938 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Residual Based A Posteriori Error Estimators for AFC Schemes for Convection-Diffusion Equations Jha, Abhinav Numerical Analysis 65N15 (primary) 65N30 (secondary) 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 Streamline Upwind Petrov Galerkin (SUPG) estimator proposed in \cite{JN13}. Numerical examples study the effectivity index and the adaptive grid refinement for two limiters in two dimensions. |
| title | A Residual Based A Posteriori Error Estimators for AFC Schemes for Convection-Diffusion Equations |
| topic | Numerical Analysis 65N15 (primary) 65N30 (secondary) |
| url | https://arxiv.org/abs/2005.02938 |