Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems
Abstract
Conforming finite element approximations of a given diffusion-convection problem with positive diffusion coefficient, incompressible convective velocity field, and a Dirichlet section of the boundary that includes all the inflow boundary are considered. The concept of symmetrization is introduced and general error bounds for a Petrov-Galerkin method are derived. Approximations based on two symmetric forms are studied, and the problem of interpreting a finite element approximation which attempts to achieve optimality in one of these symmetric forms is addressed. One and two-dimensional numerical example are included.
- Publication:
-
Computer Methods in Applied Mechanics and Engineering
- Pub Date:
- September 1984
- DOI:
- Bibcode:
- 1984CMAME..45...97B
- Keywords:
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- Computational Fluid Dynamics;
- Convective Flow;
- Diffusion Coefficient;
- Finite Element Method;
- Galerkin Method;
- Incompressible Fluids;
- Boundary Layer Flow;
- Dirichlet Problem;
- Error Analysis;
- One Dimensional Flow;
- Optimization;
- Two Dimensional Flow;
- Velocity Distribution;
- Fluid Mechanics and Heat Transfer