An upwind finite‐volume element scheme and its maximum‐principle‐preserving property for nonlinear convection–diffusion problem |
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Authors: | Fuzheng Gao Yirang Yuan Danping Yang |
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Institution: | School of Mathematics and System Science, Shandong University, Jinan 250100, Shandong, China |
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Abstract: | For a class of nonlinear convection–diffusion equation in multiple space dimensions, a kind of upwind finite‐volume element (UFVE) scheme is put forward. Some techniques, such as calculus of variations, commutating operators and prior estimates, are adopted. It is proved that the UFVE scheme is unconditionally stable and satisfies maximum principle. Optimal‐order estimates in H1‐norm are derived to determine the error in the approximate solution. Numerical results are presented to observe the performance of the scheme. Copyright © 2007 John Wiley & Sons, Ltd. |
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Keywords: | nonlinear convection– diffusion equation finite‐volume element method maximum principle upwind method |
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