Design and data structure of fully adaptive, multigrid, finite-element software
María‐Cecilia Rivara · ACM Transactions on Mathematical Software · 1984
The design and data structure of fully adaptive, multigrid, finite-element software are presented and discussed.Adaptwity is taken in a general sense to mean that optionally, sequences of finite-element problems can be constructed in the self-adaptive or quasi-interactive mode.The software combines linear, triangular, finite-element spaces; a posteriori error estimates; adaptivity of the mesh, conforming mesh-refinement algorithms for triangulations, and a full multigrid method for solving the linear systems.A molecular List data structure, which requires a minimum amount of storage, is introduced and justified.Indeed no more storage than that required to store the nonzero elements of the sequences of the (non-symmetrm) stiffness matrices is needed.As a result, an experimental, general, and flexible software is obtained.Numerical experiments performed with singular problems have shown that, in the self-adaptive mode, the numerical rate of convergence obtained approaches the maximum theoretmal rate of convergence predicted for linear elements.