Alan Demlow

Department of Mathematics
University of Kentucky

Adaptive finite element methods are popular because of their ability to efficiently approximate solutions to PDE. Essential to such methods are a posteriori error estimates which provide computable information about the discretization error. However, such a posteriori estimates are relatively rare when the desired information from the calculation requires pointwise information about the solution. We first give a basic theory for estimating pointwise gradient errors in second-order linear elliptic problems, then present a novel scheme for efficient estimation of local pointwise errors.