Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals
Qiang Du, Ben-Yu Guo, Jie Shen · SIAM Journal on Numerical Analysis · 2001
We study a Fourier-spectral method for a dissipative system modeling the flow of liquid crystals. We first prove its convergence in a suitable sense and establish the existence of a global weak solution of the original problem and its uniqueness in the two dimensional case. Then we derive error estimates which exhibit the spectral accuracy of the Fourier-spectral method. We also construct a fully discrete scheme and carry out a complete stability and error analysis for it. Finally, we present some illustrative numerical results.