Computation of potentials used in the boundary element method

Natalia Kolkovska

An  approximation to any harmonic function with known jumps across a smooth
closed curve, such as the simple and double layer logarithmic potentials,
is obtained as a solution to the discrete Laplacian on the rectangular domain.
Exact integral representations of the discrete Laplacian are used in order to
construct the right hand side of the difference equations. The error estimates
are studied under the assumption that the harmonic function belongs to some
Besov spaces.