Work

Residual Estimates for Post-processors in Elliptic Problems

Year: 2021

Type: article

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.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-021-01502-2

Authors: Andreas Dedner, Jan Giesselmann, Tristan Pryer, Jennifer K Ryan

Institutions: University of Warwick, Technische Universität Darmstadt, University of Bath, Colorado School of Mines

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,780

Funders: Deutscher Akademischer Austauschdienst, Deutsche Forschungsgemeinschaft, U.S. Air Force, Air Force Office of Scientific Research