Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case

We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, $e(x_{1})-e(x_{2})$, rather than for $e(x)$ itself. We also give a posteriori estimators for second derivatives on each element.