Esquema adaptativo para problemas tridimensionales de convección-difusión

Abstract

We present an adaptive scheme for three-dimensional convection-diffusion problems discretized by the Finite Element Method. The adaptive scheme is based on a remeshing strategy that applies a maximum volume constraint to the elements of a reference mesh. The remeshing can increase or decrease drastically the size of the elements in a single step automatically. With this strategy, the mesh quality does not deteriorate; as a consequence, the number of iterations required to solve the system of linear equations using iterative algorithms is kept constant. Two examples of very different characteristics are presented in order to analyze the proposal for a wide range of situations. The first is a three-dimensional extension of the Smolarkiewicz problem and the second is a simplified version of a point source pollutant transport problem. The results show the flexibility of the proposal. An optimal remeshing frequency, from a computational cost and accuracy of the results point of view, can be defined for both kinds of problems.