Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convectiondiffusion and KdV equations
In this paper, we provide L2 error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convectiondiffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.
65m60 65m15