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Solving the Laplace equation on the disc using the UAT spline

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  • Naimi, M.
  • Lamnii, M.

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.

Suggested Citation

  • Naimi, M. & Lamnii, M., 2025. "Solving the Laplace equation on the disc using the UAT spline," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 534-548.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:534-548
    DOI: 10.1016/j.matcom.2024.09.004
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    References listed on IDEAS

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    1. Lamnii, A. & Mraoui, H. & Sbibih, D. & Zidna, A., 2013. "Uniform tension algebraic trigonometric spline wavelets of class C2 and order four," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 68-86.
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