Properties of some weighted Sobolev spaces and application to spectral approximations. (English) Zbl 0675.65114

Bernardi, Christine; Maday, Yvon

SIAM J. Numer. Anal. 26, No. 4, 769-829 (1989).

The authors discuss the introduction of weighted Sobolev spaces on a square associated with the Jacobi weighted measure. A weighted regularity result for the Dirichlet problem associated with the Laplace operator is also discussed. Several projection operators with polynomial values are considered for which approximation results in weighted norms are stated. Finally, a collocation spectral method for the Dirichlet problem of the Laplace operator with inhomogeneous boundary condition is analyzed. It is also indicated that the authors present new results on Chebyshev approximation.

Reviewer: P.K.Mahanti

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
46M35	Abstract interpolation of topological vector spaces

Keywords:

Laplace equation; trace properties; regularity property; weighted Sobolev spaces; Jacobi weighted measure; Dirichlet problem; projection operators; collocation spectral method; Chebyshev approximation