Accuracy, convergence and stability of finite element algorithems for incompressible fluid flow

Taylor weak statement finite element CFD algorithms have been developed for the two-dimensional unsteady, incompressible Navier-Stokes equations in the form of vorticity-streamfunction, a penalty method and a new harmonic constraint formulation. A multi-dimensional (tensorial) artificial dissipative mechanism is derived and verified for effective stability control. An asymptotic rate of convergence study is conducted and compared with model problem theoretical estimates. The harmonic constraint algorithm is developed in an efficient time-accurate algorithm and proposed as a viable candidate for extension to three dimensions. The linear algebra problem associated with an embedded elliptic equation is resolved by a newly developed robust and accurate consistent sparse factorization numerical linear algebra procedure.