Abstract. In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. The advantage of meshfree methods lies in the fact, that they need no mesh generation and can thus better cope with geometric changes and high dimensional problems. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.

Received: April 8, 2011

AMS Subject Classification: 65L60, 65Pxx

Key Words and Phrases: meshfree, coupling, multiscale, inf-sup condition

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