A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis

Abstract This is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second‐order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates on the p ‐convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.