African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

An adaptive finite volume method using thin plate splines for the numerical simulation of the inviscid Burgers’ equation

  Terhemen Aboiyar
Department of Mathematics, Statistics and Computer Science, University of Agriculture, P. M. B. 2373, Makurdi, Benue State, Nigeria. 
Email: [email protected]

  •  Accepted: 26 July 2010
  •  Published: 31 August 2010

Abstract

 

 

Thin plate splines are utilized in the construction of a non-oscillatory finite volume method for the inviscid Burgers’ equation which is a prototype nonlinear conservation law. To capture the sharp features that occur during numerical simulation, the method is implemented on an adaptive triangulation. An a posteriori error indicator is used to detect regions where the solution varies rapidly.

 

Key words: Finite volume methods, WENO method, conservation laws, radial basis functions, thin plate splines.