Solving the Laplace equation on the disc using the UAT spline

M. Naimi and M. Lamnii

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 228, issue C, 534-548

Abstract: In this work, we are interested in the resolution of the Laplace equation −Δu=f with Dirichlet boundary condition in a closed surface S in R2, which is – topologically – equivalent to the unit disc D={x,y|x2+y2⩽1}. It is known that for a function u represented in polar coordinates on D, certain boundary conditions must be satisfied by u so that the surface S is of class C0. More precisely, we construct an approximant of class C0 on D as a tensor product of two quasi-interpolants, one based on UAT-splines and the other based on classical B-splines. Some numerical results are given to validate the work.

Keywords: Elliptic PDEs; B-spline; UAT spline; Quasi-interpolation; Collocation method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:228:y:2025:i:c:p:534-548

DOI: 10.1016/j.matcom.2024.09.004

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