Name
Abstract | ||
|---|---|---|
Summary. We consider singularly perturbed linear elliptic problems in two dimensions. The solutions of such problems typically exhibit
layers and are difficult to solve numerically. The streamline diffusion finite element method (SDFEM) has been proved to produce
accurate solutions away from any layers on uniform meshes, but fails to compute the boundary layers precisely. Our modified
SDFEM is implemented with piecewise linear functions on a Shishkin mesh that resolves boundary layers, and we prove that it
yields an accurate approximation of the solution both inside and outside these layers. The analysis is complicated by the
severe nonuniformity of the mesh. We give local error estimates that hold true uniformly in the perturbation parameter , provided only that , where mesh points are used. Numerical experiments support these theoretical results.
|
Year | DOI | Venue |
|---|---|---|
2001 | 10.1007/PL00005420 | Numerische Mathematik |
Keywords | Field | DocType |
piecewise linear,two dimensions,finite element method,boundary layer | Linear equation,Boundary value problem,Convection–diffusion equation,Maximum principle,Mathematical analysis,Finite element method,Singular perturbation,Streamline diffusion,Piecewise linear function,Mathematics | Journal |
Volume | Issue | ISSN |
87 | 3 | 0029-599X |
Citations | PageRank | References |
9 | 0.76 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Torsten Linß | 1 | 68 | 14.77 |
| Martin Stynes | 2 | 273 | 57.87 |