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)?
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 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.
You may want to take a look at the arXiv preprint of
- B. Keith, A. V. Astaneh, and L. Demkowicz, "Goal-oriented adaptive mesh refinement for non-symmetric functional setting."
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:
- 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.
specifically for dual-weighted residual method.