Name
Title | ||
|---|---|---|
hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems |
Abstract | ||
|---|---|---|
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 H 2. For this case we construct suitable C 1﾿-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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/978-3-642-41515-9_61 | NAA |
Field | DocType | Volume |
Boundary value problem,Second-order logic,Subspace topology,Mathematical analysis,Sobolev space,Finite element method,Boundary layer,Basis function,Mathematics,hp-FEM | Conference | 8236 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
3 | 6 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christos Xenophontos | 1 | 35 | 10.06 |
| Jens Markus Melenk | 2 | 133 | 24.18 |
| Niall Madden | 3 | 29 | 7.41 |
| L. Oberbroeckling | 4 | 8 | 1.58 |
| Pandelitsa Panaseti | 5 | 0 | 0.34 |
| Antri Zouvani | 6 | 0 | 0.34 |