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Volume 15, Issue 1-2
Conforming Mixed Triangular Prism Elements for the Linear Elasticity Problem

Jun Hu & Rui Ma

Int. J. Numer. Anal. Mod., 15 (2018), pp. 228-242.

Published online: 2018-01

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  • Abstract

We propose a family of conforming mixed triangular prism finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. These elements are constructed by product of elements on triangular meshes and elements in one dimension. The well-posedness is established for all elements with $k ≥ 1$, which are of $k+1$ order convergence for both the stress and displacement. Besides, a family of reduced stress spaces is proposed by dropping the degrees of polynomial functions associated with faces. As a result, the lowest order conforming mixed triangular prism element has 93 plus 33 degrees of freedom on each element.

  • Keywords

Mixed finite element, triangular prism element, linear elasticity.

  • AMS Subject Headings

65N30, 73C02

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hujun@math.pku.edu.cn (Jun Hu)

maruipku@gmail.com (Rui Ma)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-228, author = {Hu , Jun and Ma , Rui}, title = {Conforming Mixed Triangular Prism Elements for the Linear Elasticity Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {228--242}, abstract = {

We propose a family of conforming mixed triangular prism finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. These elements are constructed by product of elements on triangular meshes and elements in one dimension. The well-posedness is established for all elements with $k ≥ 1$, which are of $k+1$ order convergence for both the stress and displacement. Besides, a family of reduced stress spaces is proposed by dropping the degrees of polynomial functions associated with faces. As a result, the lowest order conforming mixed triangular prism element has 93 plus 33 degrees of freedom on each element.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10565.html} }
TY - JOUR T1 - Conforming Mixed Triangular Prism Elements for the Linear Elasticity Problem AU - Hu , Jun AU - Ma , Rui JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 228 EP - 242 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10565.html KW - Mixed finite element, triangular prism element, linear elasticity. AB -

We propose a family of conforming mixed triangular prism finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. These elements are constructed by product of elements on triangular meshes and elements in one dimension. The well-posedness is established for all elements with $k ≥ 1$, which are of $k+1$ order convergence for both the stress and displacement. Besides, a family of reduced stress spaces is proposed by dropping the degrees of polynomial functions associated with faces. As a result, the lowest order conforming mixed triangular prism element has 93 plus 33 degrees of freedom on each element.

Hu , Jun and Ma , Rui. (2018). Conforming Mixed Triangular Prism Elements for the Linear Elasticity Problem. International Journal of Numerical Analysis and Modeling. 15 (1-2). 228-242. doi:
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