Quadratic, streamline upwinding for finite element method solutions to 2-D convective transport problems Original Research Article

During the past decade, Finite Element Methods (FEMs) have been recognized to be more powerful tools in the solution of various flow problems as opposed to their predecessors, Finite Difference Methods. On a fundamental level, the FEM involves approximations to the solution over a given trial space on a discrete mesh, rather than Finite Difference approximations to the differential operators on a discrete mesh. In this way, the mechanics (operators) of the FEM remain closer to the physical principles associated with a given problem. In addition to this, the FEM incorporates boundary conditions very efficiently into the numerical formulation. Much current research is aimed at making these FEMs viable options for convection-dominated flows. In 1985, Mizukami et al. published two papers advancing the approach of streamline upwinding within linear elements for FEMs. The purpose of this work is to demonstrate that streamline upwinding of higher ordered elements is a more accurate option. The work goes on to show exactly how streamline upwinding effects the stability of iteratively solving the global algebraic system resulting from the FEM.