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A global mapping method for improving the performance of quadratic elements
Author(s) -
Nath B.,
Potamitis S. G.
Publication year - 1987
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.1620240204
Subject(s) - quadratic equation , convergence (economics) , finite element method , transformation (genetics) , domain (mathematical analysis) , simple (philosophy) , mathematics , mathematical optimization , computer science , space (punctuation) , algorithm , mathematical analysis , geometry , engineering , structural engineering , operating system , biochemistry , chemistry , philosophy , epistemology , economics , gene , economic growth
A simple method is proposed in this paper for improving the performance (accuracy and convergence) of quadratic elements. In this the physical domain of the problem, as well as the constitutive relationships, are transformed globally by implementing a suitable co‐ordinate transformation, and the problem is then solved in the mapped (transformed) domain using finite elements of the mapped space following the processes of the conventional FEM. Results show that the method significantly improves the performance of quadratic elements in both two and three dimensions. The mathematical implications of mapping in this way indicate that the method can also be applied for improved performance to higher‐order elements if required.