Three-dimensional superconvergent gradient recovery on tetrahedral meshes

Jie Chen; Zhangxin Chen

doi:10.1002/nme.5229

Three-dimensional superconvergent gradient recovery on tetrahedral meshes

Jie Chen^*
, Zhangxin Chen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have O(h^1+ɑ)(ɑ ≈ 0.5) superconvergence in the l₂ norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method.

Original language	English
Pages (from-to)	819-838
Number of pages	20
Journal	International Journal for Numerical Methods in Engineering
Volume	108
Issue number	8
DOIs	https://doi.org/10.1002/nme.5229
Publication status	Published - 23 Nov 2016
Externally published	Yes

Keywords

centroidal Voronoi Delaunay tessellation
finite element methods
modified superconvergence patch recovery
superconvergence

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10.1002/nme.5229

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title = "Three-dimensional superconvergent gradient recovery on tetrahedral meshes",

abstract = "In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have O(h1+ɑ)(ɑ ≈ 0.5) superconvergence in the l2 norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method.",

keywords = "centroidal Voronoi Delaunay tessellation, finite element methods, modified superconvergence patch recovery, superconvergence",

author = "Jie Chen and Zhangxin Chen",

note = "Publisher Copyright: Copyright {\textcopyright} 2016 John Wiley \& Sons, Ltd.",

year = "2016",

month = nov,

day = "23",

doi = "10.1002/nme.5229",

language = "English",

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journal = "International Journal for Numerical Methods in Engineering",

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T1 - Three-dimensional superconvergent gradient recovery on tetrahedral meshes

AU - Chen, Jie

AU - Chen, Zhangxin

PY - 2016/11/23

Y1 - 2016/11/23

N2 - In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have O(h1+ɑ)(ɑ ≈ 0.5) superconvergence in the l2 norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method.

AB - In this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three-dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have O(h1+ɑ)(ɑ ≈ 0.5) superconvergence in the l2 norm at nodes of a CVDT mesh for an arbitrary three-dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method.

KW - centroidal Voronoi Delaunay tessellation

KW - finite element methods

KW - modified superconvergence patch recovery

KW - superconvergence

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DO - 10.1002/nme.5229

M3 - Article

AN - SCOPUS:84959440227

SN - 0029-5981

VL - 108

SP - 819

EP - 838

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

IS - 8

ER -

Three-dimensional superconvergent gradient recovery on tetrahedral meshes

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