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 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Toeplitz matrix

Generating function and spectral symbol

Approximation of differential operators

Beräkningsvetenskap med inriktning mot numerisk analys

Scientific Computing with specialization in Numerical Analysis

Publication and Content Type

ref (subject category)

art (subject category)