p-version of the finite-element method. [COMET X]
In the p-version of the finite-element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached. We first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite-element triangulation. These properties lead to an a priori estimate of the asymptotic rate of convergence of the p-version. The estimate shows that the p-version gives results which are not worse than those obtained by the conventional finite-element method (called the h-version, in which h represents the maximum diameter of the elements) when quasi-uniform triangulations are employed and the basis for comparison is the number of degrees of freedom. Furthermore, in the case of a singularity problem we show (under conditions which are usually satisfied in practice) that the rate of convergence of the p-version is twice that of the h-version with quasi-uniform mesh. Inverse approximation theorems which determine the smoothness of a function based on the rate at which it is approximated by piecewise polynomials over a fixed triangulation are proved both for singular and non-singular problems. We present numerical examples which illustrate the effectiveness of the p-version for a simple one-dimensional problem and for two problems in two-dimensional elasticity. We also discuss round off error and computational costs associated with the p-version. Finally, we describe some important features, such as hierarchic basis functions, which have been utilized in COMET-X, an experimental computer implementation of the p-version.
- Research Organization:
- Washington Univ., St. Louis, MO (USA). Center for Computational Mechanics
- DOE Contract Number:
- AS05-76ER05126
- OSTI ID:
- 6028207
- Report Number(s):
- ORO-5126-83; ON: DE83013291
- Country of Publication:
- United States
- Language:
- English
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