IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Local and Global in Time Numerical Stability of Fully Discrete Pseudo-Spectral Schemes for Nonlinear PDEs

  • Aug. 31, 2011
  • 1:30 p.m.
  • LeConte 312

Abstract

Stability and convergence analysis for fully discrete pseudo spectral numerical schemes to nonlinear PDEs are presented in this talk, such as viscous Burgers' equation and incompressible Navier-Stokes equations. Related applications to incompressible Euler equation and quasi-geostrophic equation will also be addressed, in both 2-D and 3-D, for smooth and vortex sheet initial data. In addition, high order time stepping schemes, including Adams Bashforth-Adams Moulton multi-step schemes up to fourth order accuracy and high order explicit SSP schemes, will be explored in detail. Unconditional stability is established for the implicit time stepping algorithms.

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