Some recent convergence result for streamline diffusion finite element methods for time
dependent hyperbolic conservation laws are reported. For systems in several dimensions
written in entropy variables, it is proven that limits of finite element solutions are entropy
solutions of the conservation law. For the scalar Burgers' equation in one space dimension,
it is proven, using compensated compactness, that if the finite element solutions are
uniformly bounded, then a subsequence will converge to an entropy solution of Burgers' …