ARITHMETIC FOR EVALUATING 3-DIMENSIONAL H VS P FINITE-ELEMENT REFINEMENT STRATEGIES

For pth degree scalar interpolation polynomials on an n-dimensional si mplicial finite-element mesh R(n)BAR, exact formulas are derived for t he number of nonzero entries X(p)(R(n)BAR) in the finite element ''sti ffness'' matrix associated with the Dirichlet integral and D(p)(R(n)BA R), the number of degrees of freedom. For n = 1,2,3 these results are rephrased in terms of familiar data so that useful rules for h vs. p r efinement can be considered.