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The h-p version of the finite element method. II. General results and applications. (English) Zbl 0634.73059
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
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[1] Babuška, I.: Suri, M. (1986) : The optimal convergence rate of the p-version of the finite element method. (to appear)
[2] Babuška, I.; Szabo, B.A.; Katz, I.N. (1981): The p-version of finite element method. SIAM J. Num. Anal. 18; 515–545 · Zbl 0487.65059 · doi:10.1137/0718033
[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 · doi:10.1002/nme.1620180302
[4] Gignag, D.A.; Babuška, I.; Mesztenyi, C. (1983): An Introduction to the FEARS program. David W. Taylor Naval Ship Research and Development Center Report DTNSRPC/CMLD-83/04
[5] Gui, W.; Babuska, 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 BN1037, Part E : The adoptive h-p version, Tech. Note BN-1038. Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
[6] Guo, B.; Babuska, I. (1986) : The h-p version of the finite element Method. Part 1 : The basic approximation results.
[7] Computational Mech. 1, 21–41
[8] Mesztenyi, C.; Szymczak, W. (1982): FEARS users manual for UNIVAC 1100, Tech. Note BN-991, Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
[9] Vogelius, M. (1983): An analysis of the p-version of the finite element method for near incompressible materials, uniformly valid optimal error estimates. Num. Math. 41, 39–53 · Zbl 0504.65061 · doi:10.1007/BF01396304
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