Journal article
Convergence of a step-doubling galerkin method for parabolic problems
Mathematics of computation, Vol.74(251), pp.1053-1065
2005
DOI: 10.1090/S0025-5718-04-01696-5
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.
Details
- Title: Subtitle
- Convergence of a step-doubling galerkin method for parabolic problems
- Creators
- Bruce P AyatiTodd F Dupont
- Resource Type
- Journal article
- Publication Details
- Mathematics of computation, Vol.74(251), pp.1053-1065
- DOI
- 10.1090/S0025-5718-04-01696-5
- ISSN
- 0025-5718
- eISSN
- 1088-6842
- Language
- English
- Date published
- 2005
- Academic Unit
- Mathematics; Orthopedics and Rehabilitation
- Record Identifier
- 9983985707102771
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