Trace liftings which preserve polynomials. (Relèvements de traces préservant les polynômes.) (French. Abridged English version) Zbl 0755.65103

Bernardi, Christine; Dauge, Monique; Maday, Yvon

C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 333-338 (1992).

Summary: We build operators which lift polynomials on the edges of a triangle or a square into polynomials. These operators are continuous in usual Sobolev norms for the triangles and in weighted Sobolev norms for the square.

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
46G15	Functional analytic lifting theory
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

lifting operators; spectral methods; \(p\)-version of the finite element method; Sobolev spaces; trace liftings; Sobolev norms