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Zbl 0746.65072
Dawson, Clint N.; Dupont, Todd F.
Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems.
(English)
[J] Math. Comput. 58, No.197, 21-34 (1992). ISSN 0025-5718; ISSN 1088-6842/e

The authors consider several domain decomposition methods for the problem: $u\sb t-\nabla\cdot(a\nabla u)+bu=0$ on $\Omega\times (0,T]$, ${\partial u\over \partial n}=0$ on $\partial \Omega\times (0,T]$, $u(x,0)=u\sp 0(x)$ on $\Omega$, where $\Omega\in\bbfR\sp d$ is a bounded domain with smooth boundary and $n$ is the outward normal.\par The procedures use explicit calculations on the boundaries of the subdomains to predict the flux. They are also conservative in the sense that the surfaces of the subdomains do not serve as sources or sinks.\par Error estimates are given in terms of solutions of some related elliptic problems.
[E.Schechter (Kaiserslautern)]
MSC 2000:
*65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
65Y05 Parallel computation (numerical methods)
35K15 Second order parabolic equations, initial value problems

Keywords: finite elements; parallel computing; parabolic equation; domain decomposition; Error estimates

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