Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems

Some least-squares mixed finite element methods for convection-diffusion pr oblems, steady or nonstationary, are formulated, and convergence of these s chemes is analyzed. The main results are that a new optimal a priori L-2 er ror estimate of a least-squares mixed finite element method for a steady co nvection-diffusion problem is developed and that four fully-discrete least- squares mixed finite element schemes for an initial-boundary value problem of a nonlinear nonstationary convection-diffusion equation are formulated. Also, some systematic theories on convergence of these schemes are establis hed.