Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations

Abstract In this paper, we study the error estimates of local discontinuous Galerkin methods based on generalized numerical fluxes for one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain type optimal estimates. The experiments show that scheme coupled with third implicit Runge–Kutta method can achieve $(k+1)$ ( k + 1 ) th accuracy.