Stability of the Lagrange-Galerkin method: the performance of quadrature in theory and practice

Abstract

We investigate the stability properties of the Lagrange-Galerkin method using quadrature for both linear and quadratic elements. We find the regions of instability for various types of quadrature for linear advection in one dimension, and then perform numerical experiments on two test problems to assess the implications of these results for practical situations. The first problem is the familiar rotating cone problem and the second is advection in the flow field generated by the driven cavity problem.