A local in time goal oriented adaptive finite element method for combustion problems

Resumen

In this paper we shall first discuss the properties that a numerical method must possess to accurately approximate the solution of advection-diffusion-reaction equations. From this discussion it will be clear that if we require both efficiency and accuracy in the numerical simulations, then we have to use methods that will adapt to the space-time behavior of the main features of the solutions. In this respect, we shall present, in the framework of finite elements, a new goal oriented adaptive method based on duality techniques and comment on the pros and cons of this method as compared with conventional dual weighted residual adaptive methods. This method is applied to the simulation of combustion problems such as planar lifted flames and planar jets.