Implicit finite difference methods on composite grids (Q1098588)

The author considers the use of multi-component overlapping staggered grids for constructing stable implicit finite difference schemes approximating parabolic equations of the form \(u_ t=Lu\), where L is some elliptic differential operator. Overlapping grid systems are motivated by complex geometries of the objects studied as well as by the use of computers having parallel architectures. Various schemes of interaction between the grids are investigated in the paper. The local truncation error for the cases of lagged boundary values and alternating grid updating is determined by the Taylor series expansions. Numerical results allowing us to compare the strategies proposed are given for the Burger equation as model problem.