In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion 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.
|Number of pages||18|
|Journal||Computer methods in applied mechanics and engineering|
|Publication status||Published - 1 Aug 2007|
- Nonlinear convection–diffusion equation
- KdV equation
- Error estimate
- Local discontinuous Galerkin method