Weighted least-squares approximations to nonlinear hyperbolic equations

Some approximate methods for solving nonlinear hyperbolic equations are presented and analyzed. The methods consist of discretizing with respect to time and solving the resulting hyperbolic equation for fixed time by least-squares finite-element methods. Stability of appropriate weighted least-squares approximations is provided. Uniform and time varying optimal grids based on the mesh redistribution approach are considered. Numerical results for the inviscid Burgers' equation are also presented. (C) 2004 Elsevier Ltd. All rights reserved.