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Convergence of a step-doubling Galerkin method for parabolic problems
Authors:Bruce P Ayati  Todd F Dupont
Institution: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  
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