This paper presents the design, development and application of a computational infrastructure to support the implementation of parallel adaptive algorithms for the solution of sets of partial differential equations. The infrastructure is separated into multiple layers of abstraction. This paper is primarily concerned with the two lowest layersof this infrastructure: A layer which defines and implements dynamic distributed arrays (DDA), and a layer in which several dynamic data and programming abstractions are implemented in terms of the DDAs. The currently implemented abstractions are those needed for formulation of hierarchical adaptive finite difference methods, hp-adaptive finite element methods, and fast multipole method for solution of linear systems. Implementation of sample applications based on each of these methods are described and implementation issues and performance measurements are presented.