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

Karel Kovářík () and Juraj Mužík
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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

Mathematics, 2022, vol. 10, issue 20, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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