TY  - JOUR
A1  - Legatiuk, Anastasiia
A1  - Gürlebeck, Klaus
A1  - Hommel, Angela
T1  - Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice
T2  - Mathematical Methods in the Applied Sciences
N2  - 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 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.
KW  - diskrete Fourier-Transformation
KW  - Laplace-Operator
KW  - discrete fourier transform
KW  - discrete fundamental solution
KW  - laplace operator
KW  - rectangular lattice
Y1  - 2021
UR  - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/4582
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220209-45829
UR  - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7747
VL  - 2021
SP  - 1
EP  - 23
PB  - Wiley
CY  - Chichester
ER  -