The h-p version of the finite element method. II. General results and applications. (English) Zbl 0634.73059

Guo, B.; Babuška, I.

Comput. Mech. 1, 203-220 (1986).

The authors propose to study the properties of convergence of the finite element method when refining simultaneously the mesh (h) and the degree of the polynomial (p). Particular results, for special meshes and domains, are derived in part 1. In part 2 the results are generalized for curved domains and numerical experiments are presented. The main result of the articles is to show that the error of the (h-p) finite element approximation decays exponentially, the exponent being some power of the number of degrees of freedom of the system.

Reviewer: R.Sampaio

MSC:

74S05	Finite element methods applied to problems in solid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65D05	Numerical interpolation

Keywords:

h-p version of finite element method; exponential rate of convergence; curved domains

Citations:

Zbl 0634.73058; Zbl 0628.65102

References:

[1]	Babuška, I.: Suri, M. (1986) : The optimal convergence rate of the p-version of the finite element method. (to appear)
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[3]	Babuska, I.; Szabo, B.A. (1982): On the rate of convergence of finite element method, Int. J. Num. Meth. Eng. 18, 323–341 · Zbl 0498.65050
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[6]	Guo, B.; Babuska, I. (1986) : The h-p version of the finite element Method. Part 1 : The basic approximation results.
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