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The approximation of solutions of elliptic boundary-value problems via the p-version of the finite element method. (English) Zbl 0617.65109
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
Citations:
Zbl 0572.65074
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