Abstract
Characteristic Galerkin (CG) schemes were first presented for one- and two-dimensional conservation laws by Morton. In this paper, a class of modified second order accurate characteristic Petrov-Galerkin (CPG) schemes obtained by combining a unit leap function with a linear element as the try function, called a nonlinear element, are derived for one- and two-dimensional conservation laws. The schemes constructed are due to characteristic relations and the structure of the solutions, and made to have high resolution and nonoscillations. Finally, numerical experiments are given.
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