Multilevel augmentation methods for solving the Burgers' equation |
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| Authors: | Jian Chen Zhongying Chen Sirui Cheng Jiemin Zhan |
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| Institution: | 1. Department of Mathematics, Foshan University, Foshan, People's Republic of China;2. Department of Scientific Computing and Computer Applications, Sun Yat‐Sen University, Guangzhou, People's Republic of China;3. Department of Applied Mechanics and Engineering, Sun Yat‐Sen University, Guangzhou, People's Republic of China;4. Department of Mechanics and Engineering, Sun Yat‐Sen University, Guangzhou, People's Republic of China |
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| Abstract: | In this article, multilevel augmentation method (MAM) for solving the Burgers' equation is developed. The Crank–Nicolson–Galerkin scheme of the Burgers' equation results in nonlinear algebraic systems at each time step, the computational cost for solving these nonlinear systems is huge. The MAM allows us to solve the nonlinear system at a fixed initial lower level and then compensate the error by solving a linear system at the higher level. We prove that the method has the same optimal convergence order as the projection method, while reducing the computational complexity greatly. Finally, numerical experiments are presented to confirm the theoretical analysis and illustrate the efficiency of the proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1665–1691, 2015 |
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| Keywords: | Burgers' equation Crank– Nicolson– Galerkin scheme multiscale Galerkin method multilevel augmentation method nonlinear equation |
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