Application of Incremental Unknowns to the Burgers Equation
Abstract
Incremental unknowns (IU) have been introduced in Temam [ 1 ] as a means to approximate attractors and inertial manifolds when finite difference discretizations are used. It has then appeared that, for the approximation of linear elliptic problems, they produce a competitive preconditioner. Firstly this preconditioner allows an easy utilization of conjugate gradient methods with multigrid discretizations; secondly the numerical algorithm that we obtain using IU is as efficient as the V-cycle multigrid method; see Chen and Temam [ 2 - 5 ], and a survey in Temam [ 6 ].
Fields of Study & Subjects
Fluid Dynamics and Turbulent Flows
Stability and Controllability of Differential Equations
Computational Fluid Dynamics and Aerodynamics
Publication details
- Journal / source
- Computational Fluid Dynamics Techniques
- Publisher
- CRC Press
- Pages
- 729–740
- Publication date
- 20 February 2026
- Language
- EN
- Document type
- Book chapter