A Generalized Galerkin Method for Steady Convenction - Diffusion Problems with Application to Quadratic Shape Function Elements

A GENERALIZATION OF THE STANDARD GALERKIN FINITE ELEMENT METHOD IS CONSIDERED TO ENABLE IT TO DEAL SUCCESSFULLY WITH STEADY CONVECTION- DIFFUSION PROBLEMS. THE PROPOSED METHOD EMPLOYS A GENERALIZED GOVERNING EQUATION WHICH IS OBTAINED BY SUBTRACTING FROM THE ORIGINAL DIFFERENTIAL EQUATION THE SCALAR PRODUCT OF ITS GRADIENT BY A VECTOR OF FREE PARAMETERS ASSOCIATED WITH EACH OF THE COORDINATE-DIRECTIONS. THIS GENERALIZED EQUATION IS SUCCESSIVELY DISCRETIZED BY THE STANDARD BUBNOV-GALERKIN FINITE ELEMENT METHOD. THE EFFECTIVENESS OF THE METHOD IS ILLUSTRATED FOR THE CASE OF QUADRATIC LOCAL INTERPOLATIONS IN ONE AND TWO SPACE DIMENSIONS.

BELYTSCHKO T.;  SMOLINSKI P.; 

1995-03-15

JRC4026

https://publications.jrc.ec.europa.eu/repository/handle/JRC4026,