  In this paper we present a simple and accurate second order finite element
scheme to simulate the Burgers' equation on the whole real line and subjected
to initial conditions with compact support. The numerical simulations are
performed by considering a sequence of auxiliary spatially dimensionless
Dirichlet's problems parameterized by the domain's semidiameter L. Gaining
advantage from the well-known convective-diffusive effects of the Burgers'
equation, computations start by choosing L larger than the semidiameter of the
support of the initial condition and, as solution diffuses out, L is increased
appropriately. By direct comparisons between numerical and analytic solutions
and its asymptotic behavior, we conclude this simple scheme is very accurate
and can be applied to numerically investigate properties of this and similar
equations on infinite domains.
