Abstract
This article presents a hybridization of a local discontinu- ous Galerkin method (LDG) with the Ø method to capture nonlinear behavior of the advection-diffusion processes. The predetermined fixed ux selection is extended to the generalized problem-dependent ux se- lection in the LDG algorithm. The derived technique has been shown to be unconditionally stable through the L2 stability analysis. Two il- lustrative test problems are considered to demonstrate the effciency of the currently produced technique for both advection and diffiusion dom- inated processes.
| Original language | English |
|---|---|
| Pages (from-to) | 24-45 |
| Number of pages | 22 |
| Journal | Proceedings of the Institute of Mathematics and Mechanics |
| Volume | 47 |
| Issue number | 1 |
| Publication status | Published - 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.
Funding
The first author would like to thank the Science Fellowships and Grant Pro- grammes Department of TUBITAK (BIDEB) for their support to his academic research. The first author would like to thank the Science Fellowships and Grant Programmes Department of TUBITAK (BIDEB) for their support to his academic research.
| Funders | Funder number |
|---|---|
| Department of TUBITAK | |
| Programmes Department of TUBITAK |
Keywords
- Advection-diffusion processes
- Burgers equation
- Hopf-cole transformation
- Local discontinuous galerkin method
- Ø-method