The CFL Condition for Spectral Approximations to Hyperbolic Initial- Boundary Value Problems
Abstract
Study the stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients. Time is discretized by explicit multi-level or Runge-Kutta methods of order < or = 3 (forward Euler time differencing is included), and we study spatial discretizations by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. Prove that these fully explicit spectral approximations are stable provided their time-step, Delta, is restricted by the CFL-like condition, Delta < Const. 1/N-sq, where N equals teh spatial number of degrees of freedom. Give two independent proofs of this results, depending on two different choices of appropriate L-sq-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the non- periodic case. Keywords: Hyperbolic equations; Spectral approximations; Stability condition.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1990
- Accession Number
- ADA225291
Entities
People
- David Gottlieb
- Eitan Tadmor