Comparison of finite difference method and finite element method
Abstract
The performance of finite element (FEM) and finite difference equations (FDE) are compared. The smoothness of the approximate solution of FDE is determined as a power function of the order of the differential equation, while the FEM approximation must satisfy an equation in Sobolev space. Only modal values can be computed with FDE; spatial calculations are possible with FEM. FEM upwind versions are more suitable for convectiondiffusion equations, and can derive the same discretized equations as FDE. An analysis of the truncation error of the two methods shows the accuracies cannot be compared except when an exact solution is available. The configuration of each method for irregular geometries is illustrated. It is noted that more algebraic manipulation is necessary to discretize the FEM equations than needed for the FDE. Finally, it is shown that a nonuniform grid will allow more accurate solutions than a uniform grid.
 Publication:

Numerical Properties and Methodologies in Heat Transfer
 Pub Date:
 1983
 Bibcode:
 1983npmh.book...33S
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Finite Element Method;
 Heat Transfer;
 Comparison;
 Computational Grids;
 Conductive Heat Transfer;
 Differential Equations;
 Galerkin Method;
 Isoparametric Finite Elements;
 Linear Equations;
 Numerical Stability;
 Series Expansion;
 Truncation Errors;
 Fluid Mechanics and Heat Transfer