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Three-Dimensional Finite Element Superconvergent Gradient Recovery on Par6 Patterns

Three-Dimensional Finite Element Superconvergent Gradient Recovery on Par6 Patterns

Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 2 : pp. 178–194

Abstract

In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho's conjecture. We show that the linear finite element solution $u_h$ and the linear interpolation $u_I$ have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to $\nabla u$. A numerical example is presented to verify the theoretical result.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2010.32s.4

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 2 : pp. 178–194

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Superconvergence Par6 finite element method centroidal Voronoi tessellations Gersho's conjecture

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