Adaptive iterative splitting methods for convection-diffusion-reaction equations
- This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection–diffusion–reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers’ and Maxwell–Stefan diffusion equations.
| Author: | Jürgen GeiserORCiDGND, Jose L. HuesoGND, Eulalia MartínezORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-74208 |
| DOI: | https://doi.org/10.3390/math8030302 |
| Parent Title (English): | Mathematics |
| Publisher: | MDPI |
| Place of publication: | Basel |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/08/11 |
| Date of first Publication: | 2020/02/25 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | adaptive iterative splitting; convection–diffusion–reaction equations; error control; iterative solver method; nonlinear equations; operator-splitting method; time adaptive integration |
| Volume: | 8 |
| Issue: | 3, Article 302 |
| First Page: | 302-1 |
| Last Page: | 302-22 |
| Institutes/Facilities: | Lehrstuhl für Theoretische Elektrotechnik |
| open_access (DINI-Set): | open_access |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
