Implicit-explicit multistep finite element methods for nonlinear parabolic problems |
| |
Authors: | Georgios Akrivis Michel Crouzeix Charalambos Makridakis |
| |
Institution: | Department of Computer Science, University of Ioannina, 451 10 Ioannina, Greece ; IRMAR, Université de Rennes I, Campus de Beaulieu, F-35042 Rennes, France ; Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece, and IACM, Foundation for Research and Technology - Hellas, 711 10 Heraklion, Crete, Greece |
| |
Abstract: | We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient, since their implementation requires at each time step the solution of a linear system with the same matrix for all time levels. We derive optimal order error estimates. The abstract results are applied to the Kuramoto-Sivashinsky and the Cahn-Hilliard equations in one dimension, as well as to a class of reaction diffusion equations in |
| |
Keywords: | |
|
| 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》下载免费的PDF全文 |
|