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 massively parallel architectures. We review new parallel algorithms to solve two significant problems that arise in this context: the refinement mesh and the linear solver. A procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on distributed memory computers is presented. The parallelization of the solver is based on a parallel conjugate gradient method using domain decomposition. The error indicator and the resulting refinement parameters are computed in parallel.