Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation

Abstract

For convenience, this study mainly focuses on the reduced order of coefficient vectors for the classical finite spectral element Crank-Nicolson (CFSECN) solutions about the two-dimensional (2D) nonstationary Stokes problem, resulting that the reduced order model can possess the same basis functions together with same precision as the CFSECN one. To this end, the CFSECN format of the 2D nonstationary Stokes problem about vorticity function and stream function and, the existence and stability as well as error estimations for the CFSECN solutions are first proposed. Afterwards, a reduced order extrapolation finite spectral element Crank-Nicolson (ROEFSECN) model is created by means of proper orthogonal decomposition method, and the existence together with stability as well as errors of the ROEFSECN solutions is analyzed by the matrix tool, resulting that the theory analysis turns into very simple. Finally, two numerical examples are provided to confirm the correctness for the theory consequences. Therefore, the study is absolutely distinguished from the existed ones.