Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition
| Autor: | Eugene O'Riordan, José Luis Gracia |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pointwise
Numerical Analysis Applied Mathematics Numerical analysis Coordinate system Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Error function Discontinuity (linguistics) Initial value problem 0101 mathematics Convection–diffusion equation Analytic function Mathematics |
| Zdroj: | Applied Numerical Mathematics. 162:106-123 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2020.12.013 |
| Popis: | A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The difference between this analytical function and the solution of the parabolic problem is approximated numerically. A coordinate transformation is used so that a layer-adapted mesh can be aligned to the interior layer present in the solution. Numerical analysis is presented for the associated numerical method, which establishes that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the pointwise error bounds established in the paper. |
| Databáze: | OpenAIRE |
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