A new weighted upwind finite volume element method based on non‐standard covolume for time‐dependent convection–diffusion problems |
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Authors: | Fuzheng Gao Dong Liang |
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Affiliation: | 1. School of Mathematics, Shandong University, , Jinan 250100, Shandong, China;2. Department of Mathematics and Statistics, York University, , Toronto, Ontario, M3J 1P3 Canada |
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Abstract: | In modern numerical simulation of problems in energy resources and environmental science, it is important to develop efficient numerical methods for time‐dependent convection–diffusion problems. On the basis of nonstandard covolume grids, we propose a new kind of high‐order upwind finite volume element method for the problems. We first prove the stability and mass conservation in the discrete forms of the scheme. Optimal second‐order error estimate in L2‐norm in spatial step is then proved strictly. The scheme is effective for avoiding numerical diffusion and nonphysical oscillations and has second‐order accuracy. Numerical experiments are given to verify the performance of the scheme. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | convection– diffusion weighted upwind FVEM nonstandard covolume high‐order accuracy, mass conservation stability |
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