Pointwise a posteriori estimates for the finite element method

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.