Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case

The subject of this paper is the fast adaptive composite grid (FAC) method for solving variationally posed differential boundary value problems. Related to local defect corrections (LDC) and multilevel adaptive techniques (MLAT), an important difference is that FAC forces the user to specify the discrete problem on the finest composite grid — it is not rather an implicit result of the adaptive process. The advantages are that FAC can more readily meet practical objectives, does not suffer from some of the practical limitations of (“natural”) versions of LDC and MLAT, and lends itself to a simple theory. The latter is the subject of this paper.