The efficient solution of many large-scale scientific calculations depends on unstructured mesh strategies. For example, problems where the solution changes rapidly in small regions of the domain require an adaptive mesh strategy. In this paper we discuss the main algorithmic issues to be addressed with an integrated approach to solving these problems on heterogeneous parallel architectures. We review new parallel algorithms to solve two significant problems that arise in this context: the mesh refinement, partitioning and load balancing. The procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on heterogeneous computers is presented. The solver is based on the parallel conjugate gradient method. The error indicator and the resulting refinement parameters are computed in parallel.