East Asian J. Appl. Math., 15 (2025), pp. 268-289.
Published online: 2025-01
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A difference mixed finite element method based on the finite element pair $((P_0×P_1),$$(P_0×P_1),$$(P_1×P_0))×(P_1×P_1)$ for the three dimensional Poisson equation is studied. The method combines a mixed finite element discretization based on $(P_0 , P_0 , P_1 )×P_1$-element in $(x,y)$-plane and a finite difference discretization based on $(P_1,P_1,P_0)×P_1$-element in $z$-direction. This allows to transmit the finite element solution of the three dimensional Poisson equation in the direction $(x, y, z)$ into a series of finite element solution of the two dimensional Poisson equation in the direction $(x, y).$ Moreover, error estimates for the discrete approximation are derived. Numerical tests show the accuracy and efficiency for the method proposed.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-247.050224}, url = {http://global-sci.org/intro/article_detail/eajam/23750.html} }A difference mixed finite element method based on the finite element pair $((P_0×P_1),$$(P_0×P_1),$$(P_1×P_0))×(P_1×P_1)$ for the three dimensional Poisson equation is studied. The method combines a mixed finite element discretization based on $(P_0 , P_0 , P_1 )×P_1$-element in $(x,y)$-plane and a finite difference discretization based on $(P_1,P_1,P_0)×P_1$-element in $z$-direction. This allows to transmit the finite element solution of the three dimensional Poisson equation in the direction $(x, y, z)$ into a series of finite element solution of the two dimensional Poisson equation in the direction $(x, y).$ Moreover, error estimates for the discrete approximation are derived. Numerical tests show the accuracy and efficiency for the method proposed.