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Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice

  • This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this workThis paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp-estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices.show moreshow less

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Metadaten
Document Type:Article
Author: Anastasiia LegatiukORCiD, Prof. Dr. Klaus GürlebeckGND, Angela HommelGND
DOI (Cite-Link):https://doi.org/10.1002/mma.7747Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220209-45829Cite-Link
URL:https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7747
Parent Title (English):Mathematical Methods in the Applied Sciences
Publisher:Wiley
Place of publication:Chichester
Language:English
Date of Publication (online):2022/02/07
Date of first Publication:2021/08/31
Release Date:2022/02/09
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Professur Angewandte Mathematik
Volume:2021
Pagenumber:23
First Page:1
Last Page:23
Tag:discrete fourier transform; discrete fundamental solution; laplace operator; rectangular lattice
GND Keyword:diskrete Fourier-Transformation; Laplace-Operator
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell-Keine Bearbeitung (CC BY-NC-ND 4.0)