, Volume 95, Issue 1 Supplement, pp 75-88
Date: 16 Nov 2012

On optimal node and polynomial degree distribution in one-dimensional \(hp\) -FEM

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Abstract

We are concerned with the task of constructing an optimal higher-order finite element mesh under a constraint on the total number of degrees of freedom. The motivation for this work is to obtain a truly optimal higher-order finite element mesh that can be used to compare the quality of automatic adaptive algorithms. Minimized is the approximation error in a global norm. Optimization variables include the number of elements, positions of nodes, and polynomial degrees of elements. Optimization methods and software that we use are described, and numerical results are presented.

The research of the first author was supported by Czech Science Foundation Grant No. P105/10/1682. The research of the second author was partly supported by Czech Science Foundation Grant No. P105/10/1682.