Decoupled two‐grid finite element method for the time‐dependent natural convection problem I: Spatial discretization |
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| Authors: | Tong Zhang JinYun Yuan ZhiYong Si |
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| Affiliation: | 1. School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China;2. Departamento de Matemática, Universidade Federal do Paraná, Curitiba, Paraná, Brazil |
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| Abstract: | ![]()
In this article, a decoupled two grid finite element method (FEM) is proposed and analyzed for the nonsteady natural convection problem using the coarse grid numerical solutions to decouple the nonlinear coupled terms, and the corresponding optimal error estimates are derived. Compared with the standard Galerkin FEM and the usual two‐grid FEM, our algorithm not only keeps good accuracy but also saves a lot of computational cost. Some numerical examples are provided to verify the performances of the decoupled two‐grid FEM. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled two‐grid FEM for the nonsteady natural convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2135–2168, 2015 |
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| Keywords: | natural convection equations decoupled algorithm two grid method linearization |
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