TY  - JOUR
U1  - Wissenschaftlicher Artikel
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
JF  - 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.
AB  - 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  - General Engineering
KW  - General Mathematics
Y1  - 2021
SN  - 0170-4214
SS  - 0170-4214
U6  - https://doi.org/10.1002/mma.7747
DO  - https://doi.org/10.1002/mma.7747
SP  - 1
EP  - 23
S1  - 23
PB  - Wiley
ER  -