| Author | Hongyi Yu |
|---|---|
| Title | Solving parabolic problems with different time steps in different regions in space based on domain decomposition methods |
| Year | 1999 |
| Journal | Applied Numerical Mathematics |
| Volume | 30 |
| Pages | 475-491 |
| Abstract | 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 that 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. |