@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}
}
@inproceedings{KraussharConstalesGuerlebecketal.,
  author    = {Kraußhar, Rolf S{\"o}ren and Constales, Denis and G{\"u}rlebeck, Klaus and Spr{\"o}ßig, Wolfgang},
  title     = {APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2912},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29128},
  pages     = {8},
  abstract  = {The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@article{GuerlebeckLegatiukNilssonetal.,
  author    = {G{\"u}rlebeck, Klaus and Legatiuk, Dmitrii and Nilsson, Henrik and Smarsly, Kay},
  title     = {Conceptual modelling: Towards detecting modelling errors in engineering applications},
  series = {Mathematical Methods in Applied Sciences},
  journal   = {Mathematical Methods in Applied Sciences},
  doi       = {10.1002/mma.5934},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20200110-40614},
  pages     = {1 -- 10},
  abstract  = {Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer "simple" objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}