Implementation of the Lagrange-Galerkin Method for the Incompressible Navier-Stokes Equations

Abstract

This paper is concerned with the implementation of
Lagrange-Galerkin finite element aethods for the Navier-Stokes equations. A scheme is developed to efficiently handle unstructured meshes with local refinement, using a quad-tree-be.sed algorithm for geometric search. Several difficulties that arise in the construction of the right-hand sIde are discussed in detall and some useful tricks are proposed.
The resulting method is tested on the lid-driven square cavity and the vortex-shedding from a square cylinder problem, with satisfactory agreement with previous works.