Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high Reynolds number |
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| Authors: | Haiyan Su Xinlong Feng Yinnian He |
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| Affiliation: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, People's Republic of China;2. Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, People's Republic of China |
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| Abstract: | This survey enfolds rigorous analysis of the defect‐correction finite element (FE) method for the time‐dependent conduction‐convection problem which based on the Crank‐Nicolson scheme. The method consists of two steps: solve a nonlinear problem with an added artificial viscosity term on a FE grid and correct the solutions on the same grid using a linearized defect‐correction technique. The stability and optimal error estimate of the fully discrete scheme are derived. As a consequence, the effectiveness of the method to deal with high Reynolds number is illustrated in several numerical experiments. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 681–703, 2017 |
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| Keywords: | Crank‐Nicolson scheme defect‐correction method error estimate finite element method stability analysis time‐dependent conduction‐convection |
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