A note on the stability and accuracy of C n finite elements in steady diffusion‐convection problems

The paper is concerned with stability and accuracy of an n th order Lagrangian family of finite element steady‐state solutions of the diffusion‐convection equation, and furthermore is concerned with the stability and the accuracy of on m th kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pe c ( = uh / k ). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pe c for P 1,3 , and for P 2,5 the stable solution is obtained for Pe c less than 44.4.