Development and Application of the P-Version of the Finite Element Method.
Interim rept. 30 Sep 82-29 Aug 83,
WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS SCIENCE AND MATHEMATICS
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Two approaches to finite element analysis are now widely recognized in the engineering and mathematical communities. In both approaches the domain omega is divided into simple convex subdomains usually triangles or rectangles in two dimensions, and tetrahedera or bricks in three dimensions and over each sub-domain the unknown displacement field is approximated by a local basis function usually a polynomial of degree p. Basis functions are required to join continuously at boundaries of the subdomains in the case of planar or 3 dimensional elasticity, or smoothly in the case of plate bending. The difference between the two approaches lies in the manner in which convergence is achieved. The p-version of the finite element method is a new, important, computationally efficient approach to finite element analysis. It is more robust than the conventional h-version and its rate of convergence, for domains with corners and for other singularity problems, is twice that of the h-version.
- Theoretical Mathematics