Construction of null bases for the divergence operator associated with incompressible navier-stokes equations

Abstract

The dual variable method (DVM) and the divergence free finite element method (DFFEM) both significantly reduce the dimension of the system to be solved at each time step of discrete transient Navier-Stokes equations. We establish an equivalence of these two methods and investigate various approaches to finding sparse bases for the null space of operators associated with each of the methods. For the standard eight-node velocity and four-node pressure DFFEM, a basis for the divergence free subspace is constructed such that each basis function has nonzero support on at most nine contiguous elements.