Bibliography Page 1 Bibliography [1] Y. Achdou, C. Bernardi, and F. Coquel, A priori and a
posteriori analysis of finite volume dis- cretizations of Darcy’s equations, Numer. Math. 96 (2003) …

We give a general framework for deriving a posteriori error estimates for approximate
solutions of nonlinear problems. In a first step it is proven that the error of the approximate …

A numerical methodology which determines the quality (or robustness) of a posteriori error
estimators is described. The methodology accounts precisely for the factors which affect the …

Publisher Summary This chapter presents a critical survey on the approach to the solution of
the general three-dimensional eddy current problem, which originally started from the …

The objective of this paper is to introduce a general scheme for deriving a posteriori error
estimates by using duality theory of the calculus of variations. We consider variational …

The goal of this paper is to define a procedure for bounding the error in a conforming finite
element method. The new point is that this upper bound is fully explicit and can be computed …

Abstract In this article, Zienkiewicz‐Zhu estimator is analyzed for the piecewise linear finite
element approximate solution of an elliptic problem. The estimator is proved to be equivalent …

This paper is the first in a series in which we discuss computational methodologies for
checking the quality of a posteriori error estimators for finite element approximations of linear …

A posteriori error estimation for nonlinear variational problems by duality theory Page 1
Journal of Mathematical Sciences, Vol. 99, No. 1, 2000 A POSTERIORI ERROR ESTIMATION …

The adaptive finite element method (FEM) was developed in the early 1980s. The basic
concept of adaptivity developed in the FEM is that, when a physical problem is analyzed …