Variational methods in the theoretical analysis of spectral approximations. (English) Zbl 0539.65080

Canuto, Claudio; Quarteroni, Alfio

Spectral methods for partial differential equations, Proc. Symp., NASA Langley Res. Cent. 1982, 55-78 (1984).

Summary: [For the entire collection see Zbl 0534.00017.]
Stability and optimal rates of convergence for Chebyshev pseudo-spectral approximations are given. We consider elliptic problems with nonconstant coefficients and Dirichlet or Neumann-type boundary conditions. They are set into a variational form which satisfies the inf-sup conditions of Nečas-Babuška.

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

spectral methods; Stability; rates of convergence; Chebyshev pseudo- spectral approximations; variational form