A Petrov–Galerkin/modified operator formulation for convection–diffusion problems
- 5 August 1990
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 30 (2) , 331-347
- https://doi.org/10.1002/nme.1620300208
Abstract
A new Petrov–Galerkin method to deal with convection–diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self‐adjoint. The so‐called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady‐state examples on uniform and non‐uniform meshes are shown.Keywords
This publication has 9 references indexed in Scilit:
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equationsPublished by Elsevier ,2003
- Upwind techniques via variational principlesInternational Journal for Numerical Methods in Engineering, 1989
- A consistent approximate upwind Petrov-Galerkin method for convection-dominated problemsComputer Methods in Applied Mechanics and Engineering, 1988
- Petrov‐Galerkin methods for the time‐dependent convective transport equationInternational Journal for Numerical Methods in Engineering, 1986
- A new finite element formulation for computational fluid dynamics: II. Beyond SUPGComputer Methods in Applied Mechanics and Engineering, 1986
- A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problemsInternational Journal for Numerical Methods in Engineering, 1980
- An ‘upwind’ finite element scheme for two‐dimensional convective transport equationInternational Journal for Numerical Methods in Engineering, 1977
- Quadratic finite element schemes for two‐dimensional convective‐transport problemsInternational Journal for Numerical Methods in Engineering, 1977
- A General Numerical Solution of the Two-Dimensional Diffusion-Convection Equation by the Finite Element MethodWater Resources Research, 1970