Solving parabolic problems with different time steps in different regions in space based on domain decomposition methods

✍ Scribed by Hongyi Yu

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 420 KB
• Volume: 30
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(98)00092-0

✦ Synopsis

We describe a method for solving parabolic partial differential equations (PDEs) using local refinement in time. Different time steps are used in different spatial regions based on a domain decomposition finite element method. Extrapolation methods based on either a linearly implicit mid-point rule or a linearly implicit Euler method are used to integrate in time. Extrapolation methods are a better fit than BDF methods in our context since local time stepping in different spatial regions precludes history information. Some linear and nonlinear examples demonstrate the effectiveness of the method.