Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods |
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Authors: | Lulu Li Haiyan Su Xinlong Feng |
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Institution: | College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China; (L.L.); (H.S.) |
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Abstract: | In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. |
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Keywords: | defect-correction method natural convection equations adaptive methods error bound |
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