A Method of Composite Grids on a Prism with an Arbitrary Polygonal Base

The Dirichlet problem for the Laplace equation on a right prism with an arbitrary polygonal base is considered. A method of composite cubic and cylindrical grids is developed that allows one to obtain an approximate solution to this problem. Under certain conditions imposed on the smoothness of boundary values, the uniform convergence with the rate $O(h^2\ln h^{-1})$ is established for a difference solution on a composite grid with the total number of nodes $O(h^{-3}\ln h^{-1})$, where $h$ is the step of a cubic grid.

Received in May 2003