Theoretical and numerical convergence rates for some conforming finite elements

One of the major requirements of an approximate solution method is to rapidly converge to the exact solution. This paper is concerned with the rapidity of solution convergence for many conforming finite element models. Convergence rates are determined by theoretical analyses and checked by numerical investigation. Solution error plots are made for each element and in most cases these plots indicate a numerical convergence rate which is in agreement with that predicted by theory. The investigation considers only discretization errors; and the solution quantities referred to are for the system energy quantities which correspond to the eigenvalues for eigenvalue problems. The convergence rates determined are applicable to eigenvalue and static problems devoid of stress singularities.