Optimal control penalty least-square finite elements in fluid mechanics
Abstract
Finite element methods have been extensively used in applications related to the study of flows of various types. However, there remain problems which have not been completely solved with respect to stability, convergence, and accuracy, in cases involving flows of high Reynolds numbers, high Peclet numbers, and high Mach numbers. Currently employed mathematical procedures include the upwind finite element method (UFE) and the Galerkin finite element method (GFE). Both methods fail in the solution of the Tricomi equation. A description of an alternative approach is presented. The new approach attempts to overcome instabilities and nonconvergence inherent in equations with convective terms (elliptic-parabolic types in transport equation) or with nonlinear terms (elliptic-parabolic-hyperbolic types in Tricomi equation or transonic equation). The alternative approach makes use of the least-squares finite element method, taking into account penalty functions and optimal control.
- Publication:
-
3rd International Conference on Finite Elements in Flow Problems
- Pub Date:
- 1981
- Bibcode:
- 1981fifp.conf..165C
- Keywords:
-
- Computational Fluid Dynamics;
- Convective Flow;
- Finite Element Method;
- Least Squares Method;
- Optimal Control;
- Penalty Function;
- Boltzmann Transport Equation;
- Convergence;
- Error Analysis;
- Mach Number;
- Nonlinear Equations;
- Numerical Stability;
- Peclet Number;
- Reynolds Number;
- Fluid Mechanics and Heat Transfer