Residual Estimates for Post-processors in Elliptic Problems

Abstract

In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that “tweaks” a wide variety of existing post-processing techniques to enable efficient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge. We showcase our results by applying them to two classes of very popular reconstruction operators, the Smoothness-Increasing Accuracy-Conserving filter and superconvergent patch recovery. Extensive numerical tests are conducted that confirm our analytic findings.

Adaptive modelling of variably saturated seepage problems

“…The nodal values of z h are used to produce a piecewise quadratic function on T l . This technique is sometimes used as a post-processor to improve the quality of finite element approximation itself (32). We make the approximation…”

A posteriori error estimates for wave maps into spheres

“…To the best of our knowledge, no quantitative a posteriori error bounds are available for numerical approximation schemes for harmonic maps and harmonic map heat flows. Another option for spatial reconstruction might be to extend smoothing by convolution, as investigated in [23], to S 2 -valued functions.…”