Discontinuous Galerkin Methods

In this article we describe the discontinuous Galerkin method, which is a finite element method incorporating successful shock capturing finite volume techniques such as Riemann solvers, limiters, and total-variation-diminishing Runge–Kutta time discretizations, suitable for solving hyperbolic conservation law systems as well as convection-dominated convection diffusion equations such as the high Reynolds number Navier–Stokes equations. Keywords: discontinuous Galerkin method; numerical fluxes; Riemann solvers; limiters; TVD Runge–Kutta time discretization; Euler equations; Navier–Stokes equations

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