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Convergence of an element-partitioned subcycling algorithm for the semi- discrete heat equation. (English) Zbl 0653.65054
Large scale systems of type $Md'(t)+Kd(t)=F(t)$ which arise in the numerical solution of two- or three-dimensional heat equations by finite element methods are considered. Here M is a symmetric positive definite matrix and K is positive semidefinite. Solving these equations with a conditionally stable integrator requires to restrict the time-step according to the highest frequency component of the system and therefore the computation may be highly inefficient. To circumvent this drawback in the subcycling algorithms the spatial domain is partitioned into different spatial subdomains such that in some of them larger time steps can be used. Here the stability of a subcycling algorithm proposed by the authors is studied. The domain is partitioned into two subdomains which are advanced with steps $\Delta$ t and $m\Delta$ t and under some restrictions on $\Delta$ t first order convergence is established.
Reviewer: M.Calvo

65L05Initial value problems for ODE (numerical methods)
65M20Method of lines (IVP of PDE)
35K05Heat equation
34A30Linear ODE and systems, general
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