Quadratic nonconforming finite element method for 3D Stokes equations on cuboid meshes |
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| Authors: | Xin-chen Zhou Zhao-liang Meng Xiao-shan Wang Zhong-xuan Luo |
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| Institution: | 1.School of Mathematical Sciences,Dalian University of Technology,Dalian,China;2.School of Software,Dalian University of Technology,Dalian,China |
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| Abstract: | In this paper, the quadratic nonconforming brick element(MSLK element) introduced in 10] is used for the 3D Stokes equations. The instability for the mixed element pair MSLK-P_1 is analyzed, where the vector-valued MSLK element approximates the velocity and the piecewise P_1 element approximates the pressure. As a cure, we adopt the piecewise P_1 macroelement to discretize the pressure instead of the standard piecewise P_1 element on cuboid meshes. This new pair is stable and the optimal error estimate is achieved. Numerical examples verify our theoretical analysis. |
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