A WEIGHTED LEAST-SQUARES METHOD FOR FIRST-ORDER HYPERBOLIC SYSTEMS

The paper presents a generalization of the classical L(2)-norm weighte d least squares method for the numerical solution of a first-order hyp erbolic system. This alternative least squares method consists of the minimization of the weighted sum of the L(2) residuals for each equati on of the system. The order of accuracy of global conservation of each equation of the system is shown to be inversely proportional to the w eight associated with the equation. The optimal relative weights betwe en the equations are then determined in order to satisfy global conser vation of the energy of the physical system. As an application of the algorithm, the shallow water equations on an irregular domain are firs t discretized in time and then solved using Laplace modification and t he proposed least squares method.