Some aspects of adaptive grid computations

The development of two- and three-dimensional schemes for adaptive grid refinement and redistribution is considered. A basic family of data structures is described for the two-dimensional and three-dimensional refinement procedure; this appears to be close to optimal in terms of complexity, computation and storage overhead. The refinement scheme has been implemented for bilinear and biquadratic elements and applied to test problems in steady state semiconductor equations and in fluid mechanics. The grid redistribution process involves the use of optimization techniques for grid control via an error objective function. Grid smoothness and orthogonality properties are included and penalties used to enforce Jacobian constraints. Representative grid optimization calculations are given for a test problem.