An improved a posteriori error estimate for the Galerkin spectral method in one dimension

In Guo (2005) [9], the a posteriori   error estimators for Galerkin spectral methods andpp-version finite element methods in the one-dimensional case and their analysis as regards reliable and efficient properties were given. In this paper, some improved a posteriori error estimators are proposed which have simpler forms than the ones given in [9], and so can be easily calculated in practical applications. In particular, these a posteriori   error estimates are independent of any information about solutions of Galerkin spectral methods or pp-version finite element methods, and are determined solely by the known right-hand side term. It is proved that these a posteriori error estimators have the same reliability and efficiency as the ones in [9].