Analysis of slope limiters on unstructured triangular meshes

We analyze the stability and accuracy of second order limiters for the discontinuous Galerkin method on unstructured triangular meshes. We derive conditions for a limiter such that the numerical solution preserves second order accuracy and satisfies the local maximum principle. This leads to a new measure of cell size that is approximately twice as large as the radius of the inscribed circle. It is shown with numerical experiments that the resulting bound on the time step is tight. Finally, we consider various combinations of limiting points and limiting neighborhoods and present numerical experiments comparing the accuracy, stability, and efficiency of the corresponding limiters.