An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

Abstract

An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme to control the spurious oscillations when solutions have a large gradient. The L2‐stability and optimal priori error estimates for the semi‐discrete scheme in one‐ and multi‐dimensions are established. The numerical experiments demonstrate that the proposed method maintains the high order accuracy and controls the spurious oscillations well.