TY - JOUR T1 - The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension AU - Zhou , Jianwei JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 145 EP - 157 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m193 UR - https://global-sci.org/intro/article_detail/aamm/12041.html KW - AB -

In this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, $p$-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.