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Multilevel augmentation methods for solving the Burgers' equation
Author(s) -
Chen Jian,
Chen Zhongying,
Cheng Sirui,
Zhan Jiemin
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21966
Subject(s) - mathematics , burgers' equation , nonlinear system , partial differential equation , convergence (economics) , projection (relational algebra) , algebraic equation , projection method , mathematical optimization , algorithm , mathematical analysis , dykstra's projection algorithm , physics , quantum mechanics , economics , economic growth
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