Notes on PetrovGalerkin weighting functions in connection with the Scalar convectiondiffusion equation
Abstract
The finite element method for convectiondiffusion boundary value problems in one and two dimensions is discussed. The primary goal is to obtain a method giving accurate nodal values. The other purpose is didactic: the authors try to proceed in a way that very little prior knowledge about the subject is needed to understand the lines of thought. The one and twodimensional cases are treated separately. In both cases the appropriate weak form is derived starting from the boundary value problem in its strong form. In contrary to the usual treatment, the outcome of the manipulations is not only the weak form but, in addition, detailed information about the appropriate weighting functions is given. The general onedimensional case is treated first and a method which could be labelled as a conforming one is obtained. The twodimensional case turns out to be much more difficult; at least in practice. However, the authors suggest some possible approximate procedures as starting points for further studies. Finally some numerical results are given in the one and twodimensional cases. The results are compared with the ones obtained by the Galerkin, the Galerkin Gradient Least Squares (GGLS), and the streamline upwind/PetrovGalerkin (SUPG) methods.
 Publication:

Unknown
 Pub Date:
 1990
 Bibcode:
 1990npgw.rept.....F
 Keywords:

 Convective Flow;
 Diffusion;
 Finite Element Method;
 Galerkin Method;
 Scalars;
 Weighting Functions;
 Boundary Value Problems;
 Gradients;
 Least Squares Method;
 Linear Equations;
 Physics (General)