On the Conservation and Convergence to Weak Solutions of Global Schemes

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly ahnost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes. Key words, conservation laws, conservation, weak solutions, convergence Subject classification. Applied and Numerical Mathematics