IMPLEMENTATION OF THE LAGRANGE-GALERKIN METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper is concerned with the implementation of Lagrange-Galerkin finite element methods for the Navier-Stokes equations. A scheme is developed to efficiently handle unstructured meshes with local refinement, using a quad-tree-based algorithm for the geometric search. Several difficulties that arise in the construction of the right-hand side are discussed in detail and some useful tricks are proposed. The resulting method is tested on the lid-driven square cavity and the vortex shedding behind a rectangular cylinder and is found to give satisfactory agreement with previous works. A detailed analysis of the effect of time discretization is included.