## 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

### Citations:

Zbl 0723.73074; Zbl 0723.73075
Full Text:

### References:

 [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 [4] Babuška, I.; Suri, M., The $$h-p$$ version of the finite element method with quasiuniform meshes, RAIRO math. mod. and numer. anal., 21, 2, 199-238, (1987) · Zbl 0623.65113 [5] Gui, W.; Babuška, I., The $$h, p and h-p$$ versions of the finite element method in one dimension, parts 1, 2, 3, Numer. math., 49, 577-683, (1986) · Zbl 0614.65090 [6] Babuška, I.; Guo, B., The $$h-p$$ version of the finite element method for domains with the curved boundaries, () · Zbl 0655.65124 [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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