Stability and Convergence Analysis of Fully Discrete Fourier Collocation Spectral Method for 3-D Viscous Burgers' Equation

@article{Gottlieb2012StabilityAC,
  title={Stability and Convergence Analysis of Fully Discrete Fourier Collocation Spectral Method for 3-D Viscous Burgers' Equation},
  author={Sigal Gottlieb and Cheng Wang},
  journal={J. Sci. Comput.},
  year={2012},
  volume={53},
  pages={102-128}
}
This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type, despite the presence of aliasing error. The second feature of this work is the development of stable… CONTINUE READING
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