  We present a well-balanced nodal discontinuous Galerkin (DG) scheme for
compressible Euler equations with gravity. The DG scheme makes use of
discontinuous Lagrange basis functions supported at Gauss-Lobatto-Legendre
(GLL) nodes together with GLL quadrature using the same nodes. The
well-balanced property is achieved by a specific form of source term
discretization that depends on the nature of the hydrostatic solution, together
with the GLL nodes for quadrature of the source term. The scheme is able to
preserve isothermal and polytropic stationary solutions upto machine precision
on any mesh composed of quadrilateral cells and for any gravitational
potential. It is applied on several examples to demonstrate its well-balanced
property and the improved resolution of small perturbations around the
stationary solution.
