ABSTRACT
Abstract . We begin with a review of various forms of least-squares finite element approaches for boundary and evolution problems. A class of least-squares mixed finite elements is then developed and the basic properties described. Numerical experiments on a model problem indicate that the method is robust in the sense that it is not subject to the usual LBB restrictions associated with mixed Galerkin methods . This compu tation motivates a theoretical analysis and error estimates are given. We then present numerical experiments describing superconvergence of the least-squares approach for the test problem. Results of numerical experiments for other elliptic problems are al so given. The extension of the scheme to time-dependent problems is formulated and compared with Taylor-Galerkin , Petrov-Galerkin and Lax-Wendroff schemes. Numer ical studies are carried out for nonlinear systems including studies of solitary waves in the solution to the KdV equation, nonlinear reaction-diffusion systems such as Fisher's equation, and finally Navier-Stokes problems.
