@article{BR99b,
author = {Wolfgang Bangerth and Rolf Rannacher},
- title = {Finite element approximation of the acoustic wave equation: {E}rror
+ title = {Finite element approximation of the acoustic wave equation: {E}rror
control and mesh adaptation},
journal = {East--West J. Numer. Math.},
year = 1999,
}
@book{BR03,
- author = {Wolfgang Bangerth and Rolf Rannacher},
- title = {Adaptive Finite Element Methods for Differential Equations},
+ author = {Wolfgang Bangerth and Rolf Rannacher},
+ title = {Adaptive Finite Element Methods for Differential Equations},
publisher = {Birkh{\"a}user Verlag},
- year = 2003
+ year = 2003
}
@article{BR01a,
- author = {Wolfgang Bangerth and Rolf Rannacher},
- title = {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
- journal = {J. Comput. Acoustics},
- year = 2001,
- volume = 9,
- number = 2,
- pages = {575--591}
+ author = {Wolfgang Bangerth and Rolf Rannacher},
+ title = {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
+ journal = {J. Comput. Acoustics},
+ year = 2001,
+ volume = 9,
+ number = 2,
+ pages = {575--591}
}
@article{BR01,
@techreport{Bec98,
author = {Roland Becker},
- title = {Weighted Error Estimators for the Incompressible Navier-Stokes Equations},
+ title = {Weighted Error Estimators for the Incompressible {N}avier-{S}tokes Equations},
institution = {Universit{\"a}t Heidelberg},
type = {Preprint 98-20},
year = 1998
@inproceedings{BR95,
author = {Roland Becker and Rolf Rannacher},
- title = {Weighted A Posteriori Error Control in FE Methods},
+ title = {Weighted A Posteriori Error Control in {FE} Methods},
booktitle = {ENUMATH 97},
editor = {H. G. Bock et al.},
publisher = {World Scientific Publ., Singapore},
We will not discuss the derivation of these concepts in too great detail, but
will implement the main ideas in the present example program. For a thorough
introduction into the general idea, we refer to the seminal work of Becker and
-Rannacher \cite BR95, \cite BR96r, and the overview article of the same authors in
-Acta Numerica \cite BR01; the first introduces the concept of error
+Rannacher @cite BR95, @cite BR96r, and the overview article of the same authors in
+Acta Numerica @cite BR01; the first introduces the concept of error
estimation and adaptivity for general functional output for the Laplace
equation, while the second gives many examples of applications of these
concepts to a large number of other, more complicated equations. For
applications to individual types of equations, see also the publications by
-Becker \cite Bec95, \cite Bec98, Kanschat \cite Kan96, \cite FK97, Suttmeier
-\cite Sut96, \cite RS97, \cite RS98c, \cite RS99, Bangerth \cite BR99b,
-\cite Ban00w, \cite BR01a, \cite Ban02, and Hartmann \cite Har02, \cite HH01,
-\cite HH01b. All of these works, from the original introduction by Becker and
+Becker @cite Bec95, @cite Bec98, Kanschat @cite Kan96, @cite FK97, Suttmeier
+@cite Sut96, @cite RS97, @cite RS98c, @cite RS99, Bangerth @cite BR99b,
+@cite Ban00w, @cite BR01a, @cite Ban02, and Hartmann @cite Har02, @cite HH01,
+@cite HH01b. All of these works, from the original introduction by Becker and
Rannacher to individual contributions to particular equations, have later been
summarized in a book by Bangerth and Rannacher that covers all of these topics,
-see \cite BR03.
+see @cite BR03.
The basic idea is the following: in applications, one is not usually
not the most efficient way, it is simple since we already have all we need to
do that in place, and it also allows for simple experimenting. For more
efficient methods, again refer to the given literature, in particular
-\cite BR95, \cite BR03.
+@cite BR95, @cite BR03.
With this, we end the discussion of the mathematical side of this program and
turn to the actual implementation.