LEAST-SQUARES FINITE-ELEMENTS FOR 1ST-ORDER HYPERBOLIC SYSTEMS

A class of least-squres finite element methods has been developed for first-order systems and here we study this approach for hyperbolic problems. The formulation of the least-squares method is developed in detail and compared with the Petrov-Galerkin and Taylor-Galerkin procedures. A stability analysis is carried out and the extension to the nonlinear problem described. Numerical comparison studies demonstrate the performance of the method and suggest that it is a promising alternative to existing schemes. Applications considered include the convection equation, inviscid Burger's equation and shallow-water equations.