Answers are grounded in this paper and cite their sources.
In the p-version of the finite element method, the triangulation of the domain is fixed and the degree p of the local approximating polynomial is increased. This is in contrast with the h-version in which the degree p is fixed and the maximum diameter h of all triangles is allowed to go to zero. We derive a convergence result for the approximating solution to the biharmonic equation when using the p-version. This result shows that the rate of convergence for the p-version is twice that of h-version with quasi-uniform mesh in the approximation of singular solutions caused by corners. This result which applies to problems which require C¹ global continuity is analogous to an earlier result which applied to C⁰ problems. Applications to several benchmark problems in plate bending are presented. Sample results are examined and compared with theoretical predictions.
No takes yet. Share an insight, caveat, or question.
Katz et al. (1985) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: