New {/it a posteriori} error indicators based on edgewise slope-limiting are presented. Th
e $L_2$-norm is employed to measure the error of the solution gradient in both global and
element sense. A second order Newton-Cotes formula is utilized in order to decompose the l
ocal gradient error from a ${/mathbb P}_1$-finite element solution into a sum of edge cont
ributions. The gradient values at edge midpoints are interpolated from the two adjacent ve
rtices. Traditional techniques to recover a (superconvergent) nodal gradient from the cons
istent finite element gradients are reviewed. The deficiencies of standard smoothing proce
dures -- global $L_2$-projection and the Zienkiewicz-Zhu patch recovery -- as applied to n
on-smooth solutions are illustrated for simple academic configurations. The recovered grad
ient values are corrected by applying a slope limiter edge-by-edge so as to satisfy geomet
ric constraints. The direct computation of slopes at edge midpoints by means of limited av
eraging of adjacent gradient values is proposed as an inexpensive alternative. Numerical t
ests for various solution profiles in one and two space dimensions are presented to demons
trate the potential of this postprocessing procedure as an error indicator. Finally, it is
used to perform adaptive mesh refinement for compressible inviscid flow simulations.