Convergence of a step-doubling Galerkin method for parabolic problems

Ayati, Bruce; Dupont, Todd

doi:10.1090/S0025-5718-04-01696-5

Convergence of a step-doubling Galerkin method for parabolic problems
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by Bruce P. Ayati and Todd F. Dupont PDF

Math. Comp. 74 (2005), 1053-1065 Request permission

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.

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