Maximum norm error estimates of the Crank–Nicolson scheme for solving a linear moving boundary problem
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摘要
The Crank–Nicolson scheme is considered for solving a linear convection–diffusion equation with moving boundaries. The original problem is transformed into an equivalent system defined on a rectangular region by a linear transformation. Using energy techniques we show that the numerical solutions of the Crank–Nicolson scheme are unconditionally stable and convergent in the maximum norm. Numerical experiments are presented to support our theoretical results.
论文关键词:Moving boundaries,Crank–Nicolson scheme,Energy analysis,Stability,Convergence
论文评审过程:Received 19 November 2009, Revised 15 March 2010, Available online 2 April 2010.
论文官网地址:https://doi.org/10.1016/j.cam.2010.03.024