From Part I we know that standard Galerkin finite element methods on equidistant meshes yield inaccurate approximate solutions of singularly perturbed two-point boundary value problems unless a large number of mesh points are used. The same disappointing behaviour occurs arises when dealing with parabolic convection-diffusion problems, because such methods have no built-in upwinding. Finite element methods will now be developed specifically for the convection-diffusion situation, either by choosing special basis functions or by working on meshes designed for these problems.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Finite Element Methods. In: Robust Numerical Methods for Singularly Perturbed Differential Equations. Springer Series in Computational Mathematics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34467-4_6
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DOI: https://doi.org/10.1007/978-3-540-34467-4_6
Publisher Name: Springer, Berlin, Heidelberg
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