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Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes. (English) Zbl 0723.73076

The present article is the last one of a trilogy of papers [see the foregoing entries (Zbl 0723.73074; Zbl 0723.73075)] on the development of an adaptive h-p version of the finite element method.
In this presentation, the authors address the question of how mesh sizes h and spectral orders p can be chosen throughout a finite element mesh. However, it is pointed out that a systematic approach toward generating an optimal distribution of h and p for delivering solutions with a preset value of estimated error is not available. Thus, a simple approximate h-p mesh optimization technique is developed that can be used as an attempt to construct optimal meshes. In restricting the discussion to model classes of one-and two-dimensional elliptic boundary-value problems, a practical and probably efficient approximate scheme is offered leading to a trajectory in space of h-p distributions close to the optimal. Different results of applying the method to several test problems are discussed.
Reviewer: W.Ehlers (Essen)

MSC:

74S05 Finite element methods applied to problems in solid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
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[1] Demkowicz, L.; Oden, J.T.; Rachowicz, W.; Hardy, O., Toward a univeral \(h-p\) adaptive finite element strategy, part 1. constrained approximation and data structure, Comput. methods appl. mech. engrg., 77, 79-112, (1989) · Zbl 0723.73074
[2] Oden, J.T.; Demkowicz, L.; Westerman, T.A.; Rachowicz, W., Toward a universal \(h-p\) adaptive finite element strategy, part 2. A posteriori error estimates, Comput. methods appl. mech. engr., 77, 113-180, (1989) · Zbl 0723.73075
[3] Guo, B.; Babuška, I.; Guo, B.; Babuška, I., The \(h-p\) version of the finite element method, parts 1 and 2, Comput. mech., Comput. mech., 1, 203-220, (1986) · Zbl 0634.73059
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[7] Demkowicz, L.; Devloo, Ph.; Oden, J.T., On an \(h- type\) mesh refinement strategy based on minimization of interpolation errors, Comput. methods appl. mech. engrg., 53, 67-89, (1985) · Zbl 0556.73081
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