By Stefan Artlich, Wolfgang Mackens (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)
The GAMM Committee for "Efficient Numerical equipment for Partial Differential Equations" organizes seminars and workshops on matters in regards to the algorithmic therapy of partial differential equations. the subjects are discretisation tools just like the finite point and the boundary point procedure for varied form of functions in structural and fluid mechanics. specific awareness is dedicated to the complicated answer tools. The sequence of such seminars was once endured in 1995, January 20-22, with the eleventh Kiel-Seminar at the specified subject Numerical remedy of Coupled platforms on the Christian-Albrechts-University of Kiel. The seminar was once attended through a hundred scientist from nine nations. 23 lectures got, together with survey lectures. other forms of couplings are thought of during this quantity. The coupling of alternative parts could happen within the actual version. nonetheless, a coupling of subsystems may be generated via the numerical resolution procedure. basic examples of the latter type are the area decomposition (see p. 128) or subspace decomposition (p. 117). The neighborhood disorder correction process diversified discretizations of an analogous challenge on the way to increase the implications, even though the fundamental linear approach to be solved is still unchanged (p. 47). often, the purpose of the numerical coupling is to use (efficient) subsystem solvers (p. 1). the combo of other discretization concepts is pointed out on web page 59.
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Extra info for Numerical Treatment of Coupled Systems: Proceedings of the Eleventh GAMM-Seminar, Kiel, January 20–22, 1995
We will discuss the effect of a local defect correction step. Therefore, we also consider a discretization approach on composite grids without local defect correction. In this basic approach information from the global coarse grid is used on the local fine grids, but not the other way around. Comparison of the discretization errors of both methods shows that the local defect correction method yields better approximations than the basic approach. With respect to th~ accuracy of the local defect correction approximation it appears to be important at which grid points in the local regions the basic discretization is updated by a defect correction.
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From standard results in the theory of monotone operators, we gain existence and uniqueness of solutions in our model problem. Hl~c(n 2 For simplicity, we assume that 26 Discretization n is a polygon and consider finite partitions T,. of n, such that T E 7,. is (the interior of) a triangle with angles greater than a global constant > 0 and diameter hT > O. We assume that two non-identical triangles or so-called finite elements in 7,. share at most a common edge or a common vertex. With any partition 7,.