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Minimization of gradient errors of piecewise linear interpolation on simplicial meshes

✍ Scribed by Abdellatif Agouzal; Yuri V. Vassilevski

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
565 KB
Volume
199
Category
Article
ISSN
0045-7825

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✦ Synopsis

The paper is devoted to the analysis of optimal simplicial meshes which minimize the gradient error of the piecewise linear interpolation over all conformal simplicial meshes with a fixed number of cells N T . We present theoretical results on asymptotic dependencies of L p -norms of the gradient error on N T for spaces of arbitrary dimension d. Our analysis is based on a geometric representation of the gradient error of linear interpolation on a simplex and a relaxed saturation assumption. We derive a metric field M p such that a M p -quasi-uniform mesh is quasi-optimal, for arbitrary d and p 2 ]0, +∞]. Quasi-optimal meshes provide the same asymptotics of the L p -norm of the gradient error as the optimal meshes.

πŸ“œ SIMILAR VOLUMES

Superconvergent recovery of gradients of
Superconvergent recovery of gradients of piecewise linear finite element approximations on non-uniform mesh partitions
✍ Yongping Chen πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 518 KB

We propose the use of an averaging scheme, which recovers gradients from piecewise linear finite element approximations on the (1 + Ξ±)-regular triangular elements to gradients of the weak solution of a secondorder elliptic boundary value problem in the 2-dimensional space. The recovered gradients, f