The Dimensionality Reduction of Crank–Nicolson Mixed Finite Element Solution Coefficient Vectors for the Unsteady Stokes Equation

Zhendong Luo
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Zhendong Luo: School of Intelligent Manufacturing, Hunan Sany Polytechnic College, Changsha 410129, China

Mathematics, 2022, vol. 10, issue 13, 1-11

Abstract: By means of a proper orthogonal decomposition (POD) to cut down the dimensionality of unknown finite element (FE) solution coefficient vectors in the Crank–Nicolson (CN) mixed FE (CNMFE) method for two-dimensional (2D) unsteady Stokes equations in regard to vorticity stream functions, a reduced dimension recursive-CNMFE (RDR-CNMFE) method is constructed. In this case, the RDR-CNMFE method has the same FE basis functions and accuracy as the CNMFE method. The existence, stability, and errors of RDR-CNMFE solutions are analyzed by matrix analyzing, resulting in very simple theory analysis. Some numerical tries are used to check on the validity of the RDR-CNMFE method. The RDR-CNMFE method has second-order time accuracy and few unknowns so as to be able to shorten CPU runtime and retard the error cumulation in simulation calculating process, and improve real-time calculating accuracy.

Keywords: proper orthogonal decomposition; reduced-dimension recursive Crank–Nicolson mixed finite element method; unsteady Stokes equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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