Abstract
The block-grid method (see Dosiyev, 2004) for the solution of the Dirichlet problem
on polygons, when a boundary function on each side of the boundary is given from 
, 
, is analized. In the integral represetations around each singular vertex, which are
combined with the uniform grids on "nonsingular" part the boundary conditions are
taken into account with the help of integrals of Poisson type for a half-plane. It
is proved that the final uniform error is of order 
, where 
is the error of the approximation of the mentioned integrals, 
is the mesh step. For the 
-order derivatives (
) of the difference between the approximate and the exact solution in each "singular"
part 
order is obtained, here 
is the distance from the current point to the vertex in question, 
is the value of the interior angle of the 
th vertex. Finally, the method is illustrated by solving the problem in L-shaped polygon,
and a high accurate approximation for the stress intensity factor is given.
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