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Abstract
For pth degree scalar interpolation polynomials on an n-dimensional simplicial finite-element mesh R̄n, exact formulas are derived for the number of nonzero entries Xp(R̄n) in the finite element ‘‘stiffness’’ matrix associated with the Dirichlet integral and Dp(R̄n), 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 refinement can be considered.
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