## The h-p version of the finite element method. I. The basic approximation results.(English)Zbl 0634.73058

See the review of part II below (Zbl 0634.73059).

### 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 65D05 Numerical interpolation

Zbl 0634.73059
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### References:

 [1] Babuška, I.; Aziz, A. K.; Aziz, A. K. (ed.), Survey lectures on the mathematical foundations of the finite element method, 3-359, (1972), New York [2] Babuška, I.; Aziz, A. K., On the angle condition in the finite element method, SIAM J. Numer. Anal., 13, 214-226, (1976) · Zbl 0324.65046 [3] Babuška, I.; Dorr, M. R., Error estimates for the combined $$h$$ and $$p$$ version of finite element method, Numer. Math., 37, 252-277, (1981) · Zbl 0487.65058 [4] Babuška, I.; Gut, W.; Guo, B.; Szabo, B. (1986): Theory and performance of the h-p versions of the finite element method. (To appear) [5] Babuška, I.; Kellogg, R. B.; Pitkaranta, J., Direct and inverse error estimates with mesh refinement, Numer. Math., 33, 447-471, (1979) · Zbl 0423.65057 [6] Babuška, I. ; Suri, M. (1986) : The optimal convergence rate of the $$p$$-version of the finite element method. (To appear) [7] Babuška, I.; Szabo, B. A.; Katz, I. N., The $$p$$-version of the finite element method, SIAM J. Numer. Anal., 18, 515-545, (1981) · Zbl 0487.65059 [8] Bergh, I.; Lofstrom, J. (1976): Interpolation spaces. New York Berlin Heidelberg: Springer · Zbl 0344.46071 [9] Ciarlet, P.G. (1978): The finite element method for elliptic problems. Amsterdam: North-Holland · Zbl 0383.65058 [10] Dorr, M. R., The approximation theory for the $$p$$-version of the finite element method, SIAM J. Numer. Anal., 21, 1180-1207, (1985) · Zbl 0572.65074 [11] Dorr, M.R. (1986): The approximation theory for the $$p$$-version of the finite element method. SIAM J, Numer. Anal. (In print) · Zbl 0617.65109 [12] Geldfand, I.M.; Shilov, G.E. (1964): Generalized functions, vol. 2. New York: Academic Press [13] Gui, W.; Babuška, I. (1985): The h, p and h-p versions of the finite element method of one dimensional problem. Part 1: The error analysis of the $$p$$-version, Tech. Note BN-1036. Part 2 : The error analysis of the $$h$$ and h-p versions, Tech. Note BN-1037. Part 3 : The adaptive h-p version, Tech. Note BN-1038. Institute for Physical Science and Technology, University of Maryland, College Park [14] Guo, B.; Babuška, I. (1986) : Regularity of the solution of elliptic equations with piecewise analytic data. (To appear)
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