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A combined rh ‐adaptive scheme based on domain subdivision. Formulation and linear examples
Author(s) -
Askes Harm,
RodríguezFerran Antonio
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.142
Subject(s) - subdivision , discretization , domain (mathematical analysis) , set (abstract data type) , mathematical optimization , computer science , algorithm , scheme (mathematics) , coupling (piping) , process (computing) , adaptive algorithm , mathematics , engineering , mechanical engineering , mathematical analysis , civil engineering , programming language , operating system
An adaptive scheme is proposed in which the domain is split into two subdomains. One subdomain consists of regions where the discretization is refined with an h ‐adaptive approach, whereas in the other subdomain node relocation or r ‐adaptivity is used. Through this subdivision the advantageous properties of both remeshing strategies (accuracy and low computer costs, respectively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the approach suitable for coupling with various error assessment tools. Two‐dimensional linear examples where the analytical solution is known illustrate the approach. It is shown that the combined rh ‐adaptive approach is superior to its components r ‐ and h ‐adaptivity, in that higher accuracies can be obtained compared to a purely r ‐adaptive approach, while the computational costs are lower than that of a purely h ‐adaptive approach. As such, a more flexible formulation of adaptive strategies is given, in which the relative importance of attaining a pre‐set accuracy and speeding‐up the computational process can be set by the user. Copyright © 2001 John Wiley & Sons, Ltd.