Numerical analysis of a modified finite element nonlinear Galerkin method |
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Authors: | Email author" target="_blank">Yinnian?HeEmail author Huanling?Miao RMM?Mattheij Zhangxin?Chen |
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Institution: | (1) Faculty of Science, Xian Jiaotong University, Xian 710049, Peoples Republic of China;(2) Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands;(3) Department of Mathematics, Southern Methodist University, P.O. Box 750156, Dallas, TX 75275-0156, USA |
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Abstract: | Summary. A fully discrete modified finite element nonlinear Galerkin method is presented for the two-dimensional equation of Navier-Stokes type. The spatial discretization is based on two finite element spaces XH and Xh defined on a coarse grid with grid size H and a fine grid with grid size h << H, respectively; the time discretization is based on the Euler explicit scheme with respect to the nonlinear term. We analyze the stability and convergence rate of the method. Comparing with the standard finite element Galerkin method and the nonlinear Galerkin method, this method can admit a larger time step under the same convergence rate of same order. Hence this method can save a large amount of computational time. Finally, we provide some numerical tests on this method, the standard finite element Galerkin method, and the nonlinear Galerkin method, which are in a good agreement with the theoretical analysis.Mathematics Subject Classification (2000): 35Q30, 65M60, 65N30, 76D05 |
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