Local Discontinuous Galerkin Method for Time-Dependent Singularly Perturbed Semilinear Reaction-Diffusion Problems

Local discontinuous Galerkin method is considered for ime-dependent singularly perturbed semi linear problems with boundary layer. The method is equipped with a general numerical flux including two kinds of independent parameters. By virtue of the weighted estimates and suitably designed global projections, we establish optimal (k + 1)-th error estimate in a local region at a distance of 0(h log(17;)) from domain boundary. Here k is the degree of piecewise polynomials in the discontinuous finite element space and h is the maximum mesh size. Both semi-discrete LDG method and fully discrete LDG method with a third-order explicit Runge Kutta time-marching are considered. Numerical experiments support our theoretical results.