Song, Yin and Zhang (Int. J. Numer. Anal. Model. 4: 127-140, 2007) discovered a remarkable property of oscillatory finite element solutions of one-dimensional convection-diffusion problems that leads to a novel numerical method for the solution of such problems. In the present paper this property is described using several figures, then a simple proof of the phenomenon is given which is much more intuitive than the technical analysis of Song et al.
@article{702904,
title = {A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {188-196},
mrnumber = {MR3204411},
zbl = {1313.65194},
url = {http://dml.mathdoc.fr/item/702904}
}
Madden, Niall; Stynes, Martin. A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 188-196. http://gdmltest.u-ga.fr/item/702904/