CHARACTERISTIC-GALERKIN AND GALERKIN LEAST-SQUARES SPACE-TIME FORMULATIONS FOR THE ADVECTION-DIFFUSION EQUATION WITH TIME-DEPENDENT DOMAINS

For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation.