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arXiv · 2108.09086

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

Armando Coco·Sven-Erik Ekström·Giovanni Russo·Stefano Serra-Capizzano·Santina Chiara Stissi
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Abstract

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.

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Armando Coco, Sven-Erik Ekström, Giovanni Russo, Stefano Serra-Capizzano, Santina Chiara Stissi. 2021-08-20. Spectral and norm estimates for matrix sequences arising from a finite difference approximation of elliptic operators. https://doi.org/10.1016/j.laa.2023.03.005

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