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In this paper, semi-discrete numerical scheme for the approximation of theperiodic Vlasov-viscous Burgers' system is developed and analyzed. The schemeis based on the coupling of discontinuous Galerkin approximations for theVlasov equation and local discontinuous Galerkin approximations for the viscousBurgers' equation. Both these methods use generalized numerical fluxes. Theproposed scheme is both mass and momentum conservative. Based on generalizedGauss-Radau projections, optimal rates of convergence in the case of smoothcompactly supported initial data are derived. Finally, computational resultsconfirm our theoretical findings.

Discontinuous Galerkin Methods with Generalized Numerical Fluxes for the Vlasov-Viscous Burgers' System