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

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.