On the Overlapping Grid Method for Elliptic Boundary Value Problems

Composite overlapping grid methods were studied by Volkov [ Proceedings of the Steklov Institute of Mathematics, 96 (1968), pp. 145--185] and Starius [ Numer. Math., 28 (1977), pp. 243--258] more than 20 years ago. More recently several authors have used such methods for a variety of problems (not necessarily elliptic BVPs). This work is motivated by the recent work of Chesshire and Henshaw [ J. Comp. Phys., 90 (1990), pp. 1--64], who developed general software and have carried out extensive computational studies. This report is limited to the case where the finite difference operators are of positive type. However, within that class of problems we present a general theory.

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