Applications in Multi-Dimensional Domains

  • Jie ShenEmail author
  • Tao Tang
  • Li-Lian Wang
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 41)


We consider in this chapter several multi-dimensional problems, which (a) are of current interest; (b) are suitable for spectral approximations; and (c) can be efficiently solved by using the basic spectral algorithms developed in previous chapters. These include steady state problems: the Helmholtz equation for acoustic scattering and the Stokes equations, as well as time-dependent problems including the Allen-Cahn equation, the Cahn–Hilliard equation, the Navier–Stokes equations, and the Gross–Pitaevskii equation. For applications of spectral methods to other multidimensional problems in science and engineering, we refer, for instance, to Boyd (2001), Canuto et al. (2006), Hesthaven et al. (2007) and the references therein.


Stokes Equation Spectral Method Helmholtz Equation Stokes Problem Spectral Element Method 
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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloonHong Kong SAR
  3. 3.Division of Mathematical Sciences School of Physical & Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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