  When approximating elliptic problems by using specialized approximation
techniques, we obtain large structured matrices whose analysis provides
information on the stability of the method. Here we provide spectral and norm
estimates for matrix sequences arising from the approximation of the Laplacian
via ad hoc finite differences. The analysis involves several tools from matrix
theory and in particular from the setting of Toeplitz operators and Generalized
Locally Toeplitz matrix sequences. Several numerical experiments are conducted,
which confirm the correctness of the theoretical findings.
