TY - JOUR
T1 - Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations
JO - Communications in Computational Physics
VL - 3
SP - 838
EP - 854
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0208
UR - https://global-sci.org/intro/article_detail/cicp/13149.html
KW - Unconditionally optimal error estimates, linearized Galerkin finite element method,
Kuramoto-Tsuzuki equation, high-dimensional nonlinear problems.
AB - <p style="text-align: justify;">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.</p>