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The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation

Author

Listed:
  • Karel Kovářík

    (Department of Geotechnics, Faculty of Civil Engineering, University of Žilina, 01026 Žilina, Slovakia)

  • Juraj Mužík

    (Department of Geotechnics, Faculty of Civil Engineering, University of Žilina, 01026 Žilina, Slovakia)

Abstract

This paper deals with a new modification of the local boundary knots method (LBKM), which will allow the irregular node distribution and the arbitrary shape of the solution domain. Unlike previous localizations, it has no requirements on the number of nodes in the support or on the number of virtual points. Owing to the limited number of virtual points, the condition number of boundary knots matrix remains relatively low. The article contains the derivation of the relations of the method for steady and unsteady states and shows its effectiveness in three control examples.

Suggested Citation

  • Karel Kovářík & Juraj Mužík, 2022. "The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3855-:d:945318
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