Spectral and norm estimates for matrix-sequences arising from a finite difference approximation of elliptic operators

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