Adaptive selection of polynomial degrees on a finite element mesh

Bertóti, E.; Szabó, Barna

doi:10.1002/(sici)1097-0207(19980615)42:3<561::aid-nme379>3.3.co;2-z

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2004

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“…The problem of hp-adaptivity was addressed in the papers , Oden et al (1989), , and Demkowicz, Rachowicz and Devloo (2002). The design of p-adaptive methods for elliptic problems was addressed in Bertóti and Szabó (1998). The problem of combining p-and hp-methods with boundary element methods (BEMs) for the solution of elastic scattering problems is discussed in Demkowicz and Oden (1996).…”

Section: Discussionmentioning

confidence: 99%

Thep‐Version of the Finite Element Method

Szabó

Düster

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2004

Encyclopedia of Computational Mechanics

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The basic algorithmic structure and performance characteristics of the p ‐version of the finite element method are surveyed with reference to elliptic problems in solid mechanics. For this class of problems, the theoretical basis of the p ‐version is fully established, and a very substantial amount of engineering experience covering linear and nonlinear applications is available. It is shown that p ‐extensions on properly designed meshes make realization of exponential rates of convergence in practical computations possible and provide for the estimation and control of relative errors in terms of any data of interest. Given the growing demand for verified numerical solutions, the p ‐version is expected to play an increasingly important role in the development of future finite element software products.

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Section: Discussionmentioning

confidence: 99%