Maximum norm error estimates of the Crank–Nicolson scheme for solving a linear moving boundary problem

✍ Scribed by Wan-Rong Cao; Zhi-Zhong Sun

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 354 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.03.024

✦ Synopsis

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.