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Article

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

by
Karel Kovářík
* and
Juraj Mužík
Department of Geotechnics, Faculty of Civil Engineering, University of Žilina, 01026 Žilina, Slovakia
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(20), 3855; https://doi.org/10.3390/math10203855
Submission received: 15 September 2022 / Revised: 12 October 2022 / Accepted: 14 October 2022 / Published: 18 October 2022
(This article belongs to the Topic Fluid Mechanics)
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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.
Keywords: boundary knots method; particular solution; finite collocation; advection–diffusion boundary knots method; particular solution; finite collocation; advection–diffusion

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MDPI and ACS Style

Kovářík, K.; Mužík, J. The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation. Mathematics 2022, 10, 3855. https://doi.org/10.3390/math10203855

AMA Style

Kovářík K, Mužík J. The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation. Mathematics. 2022; 10(20):3855. https://doi.org/10.3390/math10203855

Chicago/Turabian Style

Kovářík, Karel, and Juraj Mužík. 2022. "The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation" Mathematics 10, no. 20: 3855. https://doi.org/10.3390/math10203855

APA Style

Kovářík, K., & Mužík, J. (2022). The Modified Local Boundary Knots Method for Solution of the Two-Dimensional Advection–Diffusion Equation. Mathematics, 10(20), 3855. https://doi.org/10.3390/math10203855

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