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The h-p version of the finite element method for domains with curved boundaries. (English) Zbl 0655.65124
The authors treat the convergence analysis of the h-p version of the finite element method for elliptic problems on curved domains. The advantages of the h-p version enthusiastically demonstrated (theoretically and numerically) by the authors with Theorem 5.3 serving as the celebrity are as follows: (i) The h-p version simultaneously refines the mesh and increases the degree of elements either uniformly or selectively. Furthermore, for all elliptic problems with piecewise analytic data the proper choices of meshes and elements degrees lead to an exponential rate of convergence. (ii) The h-p version is very robust with respect to the form of the elements. (iii) The h-p version provides realistic estimates in the range of engineering accuracy.
Reviewer: M.A.Ibiejugba

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
35J25 Boundary value problems for second-order elliptic equations
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