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.…
Document Type: | Article |
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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): | Creative Commons 4.0 - Namensnennung-Nicht kommerziell-Keine Bearbeitung (CC BY-NC-ND 4.0) |