Volume 21, Issue 4
Nonconforming Finite Element Method Applied to the Driven Cavity Problem

Commun. Comput. Phys., 21 (2017), pp. 1012-1038.

Published online: 2018-04

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• Abstract

A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangular meshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$ is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

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@Article{CiCP-21-1012, author = {}, title = {Nonconforming Finite Element Method Applied to the Driven Cavity Problem}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {4}, pages = {1012--1038}, abstract = {

A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangular meshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$ is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0039}, url = {http://global-sci.org/intro/article_detail/cicp/11269.html} }
TY - JOUR T1 - Nonconforming Finite Element Method Applied to the Driven Cavity Problem JO - Communications in Computational Physics VL - 4 SP - 1012 EP - 1038 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0039 UR - https://global-sci.org/intro/article_detail/cicp/11269.html KW - AB -

A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangular meshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$ is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

Roktaek Lim & Dongwoo Sheen. (2020). Nonconforming Finite Element Method Applied to the Driven Cavity Problem. Communications in Computational Physics. 21 (4). 1012-1038. doi:10.4208/cicp.OA-2016-0039
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