We describe a fine-grained, element-based data migration system that dynamically maintains global load balance on massively parallel MIMD computers, and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method supports a large class of finite element and finite difference based applications and provides an automatic element management system to which applications are easily integrated. We test the system's effectiveness with an adaptive order (-) refinement Discontinuous Galerkin finite element method for the solution of hyperbolic conservation laws on a 1024-processor nCUBE2. The results show the significant reduction in execution time synergistically obtained by combining the automatic data migration system and the adaptive finite element method.