Name
Title | ||
|---|---|---|
Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning. |
Abstract | ||
|---|---|---|
A linear one-dimensional convection–diffusion problem with a small singular perturbation parameter ε is considered. The problem is discretized using finite-difference schemes on the Shishkin mesh. Generally speaking, such discretizations are not consistent uniformly in ε, so ε-uniform convergence cannot be proved by the classical approach based on ε-uniform stability and ε-uniform consistency. This is why previous proofs of convergence have introduced non-classical techniques (e.g., specially chosen barrier functions). In the present paper, we show for the first time that one can prove optimal convergence inside the classical framework: a suitable preconditioning of the discrete system is shown to yield a method that, uniformly in ε, is both consistent and stable. Using this technique, optimal error bounds are obtained for the upwind and hybrid finite-difference schemes. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2018.02.012 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
65L10,65L12,65L20,65L70 | Convergence (routing),Discretization,Convection–diffusion equation,Mathematical analysis,Uniform convergence,Singular perturbation,Mathematical proof,Discrete system,Mathematics | Journal |
Volume | Issue | ISSN |
338 | C | 0377-0427 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thái Anh Nhan | 1 | 0 | 1.01 |
| Martin Stynes | 2 | 273 | 57.87 |
| Relja Vulanovic | 3 | 35 | 13.39 |