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Good references for dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)

Computational Science Asked on November 8, 2020

Can anyone help me with good references (books or papers) where I can learn about dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)?

2 Answers

The canonical "first" reference for the method is a paper by Becker and Rannacher that was ultimately published as an article in the ENUMATH 97 proceedings, but is often cited as the following preprint:

R. Becker, R. Rannacher: "A feed-back approach to error control in finite element methods: basic analysis and examples". IWR preprint, University of Heidelberg, 1996.

Because of the difficulty of actually locating this preprint, Becker and Rannacher later wrote a longer article on the subject in Acta Numerica:

R. Becker, R. Rannacher, "An optimal control approach to a posteriori error estimation in finite element methods," Acta Numerica, vol. 10, pp. 1–102, May 2001.

Then Rannacher thought "Why stop at 102 pages if I could write a whole book about the subject", and this led to the following book (disclaimer, if it's not obvious: I'm one of the co-authors):

W. Bangerth, R. Rannacher: "Adaptive finite element methods for differential equations". Birkhäuser, 2003.

I believe that these are the three most frequently cited resources on the DWR method for error estimation and mesh adaptation.

Correct answer by Wolfgang Bangerth on November 8, 2020

You may want to take a look at the arXiv preprint of

In this article, the authors motivate and present a new duality theory for FEM. Some overview of dual-weighted residual is also given (Section 5).

It also links to the very widely cited:

specifically for dual-weighted residual method.

Answered by Anton Menshov on November 8, 2020

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