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Article

Madden, Niall ; Stynes, Martin
A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 188-196
MSC: 34B05, 65L10, 65L60 | MR 3204411 | Zbl 1313.65194
Keywords:
piecewise linear function; Galerkin finite element method; numerical examples; one-dimensional convection-diffusion problems
Summary:
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.
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