Accuracy of the difference scheme of solving the eigenvalue problem for the Laplacian

The finite-difference approximation of the eigenvalue problem with the Dirichlet boundary conditions for the Laplacian in a two-dimensional domain of complex form is analyzed for accuracy and the error of eigenfunctions from the class W₂²( W) W_2^2\left( \Omega \right) in the mesh norm of W₂¹( w) W_2^1\left( \omega \right) is estimated.