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We present a high order scheme for approximating kinetic equations with stiffrelaxation. The objective is to provide efficient methods for solving theunderlying system of conservation laws. The construction is based on severalingredients: (i) a high order implicit upwind Discontinuous Galerkinapproximation of the kinetic equations with easy-to-solve triangular linearsystems; (ii) a second order asymptotic-preserving time integration based onsymmetry arguments; (iii) a palindromic composition of the second order methodfor achieving higher orders in time. The method is then tested at orders 2, 4and 6. It is asymptotic-preserving with respect to the stiff relaxation andaccepts high CFL numbers.

Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation