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

TLDR

The paper introduces a two‑part study on error analysis and adaptive processes for finite element calculations. Part I develops theory and methods for deriving error estimates for second‑order problems, while Part II presents adaptive refinement strategies focusing on p‑convergent methods. The authors demonstrate that these procedures achieve extremely high convergence rates in practical problems and illustrate their effectiveness through realistic stress‑analysis applications.

Abstract

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.