An Elementary method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations
Provides a general theoretical framework for error estimation in PDEs, but the approach is incremental as it extends existing functional analysis techniques.
The paper presents a simple method for deriving a posteriori error equalities and estimates for linear elliptic and parabolic PDEs, measured in a combined norm of primal and dual variables, without relying on specific numerical methods.
In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal and dual variables. We work only on the continuous (often called functional) level and do not suppose any specific properties of numerical methods and discretizations.