Discrete analogs of boundary integral equations for elliptic boundary value problems

Discrete analogs of the first and the second Green formulae are presented for the finite element approximations of elliptic boundary value problems. Using these formulae and the inverse of the discrete operator in the infinite domain discrete boundary equations analogous to the continuous boundary integral equations are constructed. We focus our attention on the discrete boundary equations with selfadjoint operators. To construct the inverse of the discrete operator in the infinite domain the apparatus of discrete fundamental solutions is used. Effective numerical technique for calculation of the discrete fundamental solutions is introduced.