aSchool of Electrical Engineering, Ulsan University, Ulsan 680-749, Korea
bDepartment of Mathematics Education, Seoul National University, Seoul 151-748, Korea
Abstract:
A priori error estimates for the Rosenau equation, which is a K-dV like Rosenau equation modelled to describe the dynamics of dense discrete systems, have been studied by one of the authors. But since a priori error bounds contain the unknown solution and its derivatives, it is not effective to control error bounds with only a given step size. Thus we need to estimate a posteriori errors in order to control accuracy of approximate solutions using variable step sizes. A posteriori error estimates of the Rosenau equation are obtained by a discontinuous Galerkin method and the stability analysis is discussed for the dual problem. Numerical results on a posteriori error and wave propagation are given, which are obtained by using various spatial and temporal meshes controlled automatically by a posteriori error.