A node-moving algorithm with application to Burgers equation and the Moltz problem

Abstract

Burgers' equation models nonlinear wave behaviour; a typical solution exhibits a steep wavefront which is difficult to represent or resolve using traditional finite difference or finite element methods. By using a finite element mesh having dynamic nodes good results for Burgers' equation are obtained using very few elements. The method developed yields a one to one mapping from some initial nodal distribution (usually uniform) to a different nodal distribution reflecting properties of the solution. The method is applied to the Moltz problem, which is a two-dimensional potential problem where there is a boundary singularity. The initial uniform mesh changes to one in which the nodes concentrate around the singularity, resulting in a more accurate solution.