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We apply two discontinuous finite element methods to the inviscid Burgers' equation and to the full equation with viscosity. In both cases we compare with a continuous space-time finite element method previously studied. For v = 0 discontinuous methods give better results, while the reverse prevails for the viscous equation.

We describe several numerical methods of computing the solutions of initial-boundary value problems for Burgers' equations in two space dimensions. The finite element method, which is a straightforward extension of its analog in one space dimension, is very efficient compared to the other methods, namely the method of lines and a Runge-Kutta-type method as studied by Crouzeix.