@article{LegatiukGuerlebeckHommel,
  author    = {Legatiuk, Anastasiia and G{\"u}rlebeck, Klaus and Hommel, Angela},
  title     = {Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice},
  series = {Mathematical Methods in the Applied Sciences},
  volume    = {2021},
  journal   = {Mathematical Methods in the Applied Sciences},
  publisher = {Wiley},
  address   = {Chichester},
  doi       = {10.1002/mma.7747},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45829},
  pages     = {1 -- 23},
  abstract  = {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.},
  subject      = {diskrete Fourier-Transformation},
  language  = {en}
}