hp finite element methods for fourth order singularly perturbed boundary value problems
Date
2013Author
Xenophontos, Christos A.Melenk, M.
Madden, N.
Oberbroeckling, L.
Panaseti, Pandelitsa
Zouvani, A.
ISSN
0302-9743Source
5th International Conference on Numerical Analysis and Applications, NAA 2012Volume
8236 LNCSPages
532-539Google Scholar check
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We consider fourth order singularly perturbed boundary value problems (BVPs) in one-dimension and the approximation of their solution by the hp version of the Finite Element Method (FEM). If the given problem's boundary conditions are suitable for writing the BVP as a second order system, then we construct an hp FEM on the so-called Spectral Boundary Layer Mesh that gives a robust approximation that converges exponentially in the energy norm, provided the data of the problem is analytic. We also consider the case when the BVP is not written as a second order system and the approximation belongs to a finite dimensional subspace of the Sobolev space H2. For this case we construct suitable C1-conforming hierarchical basis functions for the approximation and we again illustrate that the hp FEM on the Spectral Boundary Layer Mesh yields a robust approximation that converges exponentially. A numerical example that validates the theory is also presented. © 2013 Springer-Verlag.
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