Error estimates of spectral element methods with generalized Jacobi polynomials on an interval

Based on the generalized Jacobi polynomials with indices (−1,−1), a new upper bound for a posteriori error estimates is proposed, investigated and implemented for generalized Jacobi-Galerkin spectral element approximations. To simplify discussion for the error estimates, the second-order partial differential equation with homogeneous Dirichlet boundary conditions is considered on a unit interval.