High-order discontinuous Galerkin method with Lagrange multipliers for advection-diffusion problems
Abstract/Contents
- Abstract
- A high-order discontinuous Galerkin method with Lagrange multipliers (DGLM) is proposed for solving the advection-diffusion equation on unstructured meshes. Following the same methodology as the discontinuous enrichment method (DEM), free-space solutions of the governing homogeneous partial differential equation are used in lieu of standard polynomials in order to finely capture features of the solution. Polynomial Lagrange multipliers are used to enforce weak continuity of the solution at the element interfaces. The design of arbitrary-order elements for homogeneous problems is discussed in detail and is supported by a mathematical analysis. For solving non-homogeneous advection-diffusion problems, a novel approach is proposed to decrease the computational cost. Adaptivity of the method is highlighted by the use of an a posteriori error estimate for automatic mesh refinement. The numerical results reveal that these DGLM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Brogniez, Sebastien |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics |
| Primary advisor | Farhat, Charbel |
| Thesis advisor | Farhat, Charbel |
| Thesis advisor | Jameson, Antony, 1934- |
| Thesis advisor | Lew, Adrian |
| Advisor | Jameson, Antony, 1934- |
| Advisor | Lew, Adrian |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sébastien Brogniez. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Sebastien Brogniez
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...