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 the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain the linear type of optimal error estimates. The numerical experiments show that the scheme coupled with the third order implicit Runge–Kutta method can achieve the optimal (k+1)th order of accuracy.