Weighted least-squares approximationsto 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 Burgersʹ equation are also presented.