The principal term in the expansion of the error of the eigenvalues of the discrete analogue of an elliptic operator (Q1311543)

The error of the approximation for the eigenvalues of a second-order elliptic operator with variable coefficients in the main part and homogeneous Dirichlet conditions, found by an (usual) difference approximation in a plane rectangle, is of order \(h^ 2\) in the step \(h\). The \(h^ 2\)-term of the error is given in (integral) terms of the corresponding approximate eigenfunction. The results continue the previous investigations of the author [ibid. 31, No. 3, 372-380 (1991; Zbl 0733.65062) and ibid. 31, No. 4, 618-622 (1991; Zbl 0726.65119)].