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

Cite this

Chen, J., & Chen, Z. (2016). Three-dimensional superconvergent gradient recovery on tetrahedral meshes. International Journal for Numerical Methods in Engineering, 108(8), 819-838. https://doi.org/10.1002/nme.5229

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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.",

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author = "Jie Chen and Zhangxin Chen",

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year = "2016",

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AU - Chen, Zhangxin

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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.

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Three-dimensional superconvergent gradient recovery on tetrahedral meshes

Abstract

Keywords

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