The approximation of solutions of elliptic boundary-value problems via the p-version of the finite element method. (English) Zbl 0617.65109

Dorr, Milo R.

SIAM J. Numer. Anal. 23, 58-77 (1986).

The purpose of the present paper is to show how the results of the author [ibid. 21, 1180-1207 (1984; Zbl 0572.65074)] may be used to determine the approximability of some model problems in the usual Sobolev spaces by piecewise polynomials satisfying appropriate boundary and conformality conditions. Numerical results for two-dimensional linear elasticity are presented. The computations show that the predicted order of convergence is achieved even for low values of p. Some practical implications of the p-version convergence for the solvability of elliptic problems with strong singularities are also discussed.

Reviewer: J.Lovíšek

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05	Finite element methods applied to problems in solid mechanics
74B05	Classical linear elasticity
35J25	Boundary value problems for second-order elliptic equations

Keywords:

p-version of the finite element method; polygonal domains; polyhedra; Sobolev spaces; order of convergence; strong singularities

Citations:

Zbl 0572.65074