Convergence of a step-doubling Galerkin method for parabolic problems |
| |
| Authors: | Bruce P. Ayati Todd F. Dupont. |
| |
| Affiliation: | Department of Mathematics, Southern Methodist University, Dallas, Texas 75275 ; Departments of Computer Science and Mathematics, The University of Chicago, Chicago, Illinois 60637 |
| |
| Abstract: | We analyze a single step method for solving second-order parabolic initial-boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with those of Crank-Nicolson, as well as those of more general extrapolated theta-weighted schemes. We provide an example computation that illustrates both the use of step-doubling for adaptive time step control and the application of step-doubling to a nonlinear system. |
| |
| Keywords: | Variable time steps step-size control parabolic partial differential equation. |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
|
点击此处可从《Mathematics of Computation》下载全文 |
