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Volume 14, Issue 4-5
A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations

Min Zhang & Shangyou Zhang

Int. J. Numer. Anal. Mod., 14 (2017), pp. 730-743.

Published online: 2017-08

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  • Abstract

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup condition is valid and the discrete Korn inequality holds uniformly in the mesh-size. Based on these results we give some numerical verification. In addition, this element is compared numerically with six other mixed finite elements.

  • Keywords

Mixed finite element, symmetric stress, Korn's inequality, Stokes equations.

  • AMS Subject Headings

5M60, 65N30, 76M10, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-730, author = {Min Zhang and Shangyou Zhang}, title = {A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {730--743}, abstract = {

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup condition is valid and the discrete Korn inequality holds uniformly in the mesh-size. Based on these results we give some numerical verification. In addition, this element is compared numerically with six other mixed finite elements.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10058.html} }
TY - JOUR T1 - A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations AU - Min Zhang & Shangyou Zhang JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 730 EP - 743 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10058.html KW - Mixed finite element, symmetric stress, Korn's inequality, Stokes equations. AB -

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup condition is valid and the discrete Korn inequality holds uniformly in the mesh-size. Based on these results we give some numerical verification. In addition, this element is compared numerically with six other mixed finite elements.

Min Zhang and Shangyou Zhang. (2017). A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations. International Journal of Numerical Analysis and Modeling. 14 (4-5). 730-743. doi:
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