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How to Choose Basis Functions in Meshless Methods?

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Book cover Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

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Abstract

Technical progress in construction of computers, their higher speed, and larger memory gave possibility to develop new numerical methods for solution of boundary value problems. A lot of meshless methods have been developed in last years. Some of them are in a way identical with the Galerkin method, where the trial space is formed by especially constructed functions. The choice of the proper trial space is important, because the error in the Galerkin method is determined by the fact how well the exact solution can be approximated by the elements from this finite dimensional space.

In this contribution different trial spaces are considered. We will construct spaces generated by means of B-splines and shape functions received by means of the RKP technique. Examples of using trial spaces mentioned for solution of some boundary value problems will be given. We focus our attention on error estimates in these cases too.

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Author information

Authors and Affiliations

  1. Institute of Exact Science, Moravian University, Jeremenkova 42, 772 00, Olomouc, Czech Republic

    Vratislava Mošová

Authors
  1. Vratislava Mošová
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Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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Mošová, V. (2009). How to Choose Basis Functions in Meshless Methods?. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_48

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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