The error associated with a numerical solution is intimately related with
the residual, that is the lack of verification of the equation by the approximated
solution. The residual is computable but obtaining the exact error from the residual
is as difficult as computing the exact solution. Residual type estimators provide
error assessment tools based on post processing the residual. This post process is
either explicit (integrating the residual) or implicit (solving local problems with the
resid...
The error associated with a numerical solution is intimately related with
the residual, that is the lack of verification of the equation by the approximated
solution. The residual is computable but obtaining the exact error from the residual
is as difficult as computing the exact solution. Residual type estimators provide
error assessment tools based on post processing the residual. This post process is
either explicit (integrating the residual) or implicit (solving local problems with the
residual as source term). Some of the residual type estimates are guaranteed error
bounds. The standard estimators aim at assessing the energy norm of the error. Goaloriented
assessment is carried out by considering an auxiliary problem associated
with the selected quantity of interest (the adjoint or dual problem). Thus, an error
representation allows estimating the error in the quantity of interest as a post-process
of the energy measures of the errors in both the original problem and the adjoint one.
Citation
Chamoin, L., Diez, P. Preface. A: "Verifying Calculations: forty years on". Springer, 2016, p. V-VI.