Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations
Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 838–854
Abstract
This paper is concerned with unconditionally optimal error estimate of the linearized Galerkin finite element method for solving the two-dimensional and three-dimensional Kuramoto-Tsuzuki equations, while the classical analysis for these nonlinear problems always requires certain time-step restrictions dependent on the spatial mesh size. The key to our analysis is to obtain the boundedness of the numerical approximation in the maximum norm, by using error estimates in certain norms in the different time level, the corresponding Sobolev embedding theorem, and the inverse inequality. Numerical examples in both 2D and 3D nonlinear problems are given to confirm our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0208
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 838–854
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Unconditionally optimal error estimates linearized Galerkin finite element method Kuramoto-Tsuzuki equation high-dimensional nonlinear problems.