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Equivalent Legendre polynomials: Numerical integration of discontinuous functions in the finite element methods
Publikationstyp
Journal Article
Date Issued
2019-01
Sprache
English
Author(s)
TORE-URI
Volume
343
Start Page
690
End Page
720
Citation
Computer Methods in Applied Mechanics and Engineering (343): 690-720 (2019-01)
Publisher DOI
Scopus ID
The efficiency of numerical integration of discontinuous functions is a challenge for many different computational methods. To overcome this problem, we introduce an efficient and simple numerical method for the integration of discontinuous functions on an arbitrary domain. In the proposed method, the discontinuous function over the domain is replaced by a continuous equivalent function using Legendre polynomials. The method is applicable to all Ansatz spaces with continuous basis functions, and it allows to use standard numerical integration methods in the entire domain. This imposed continuous function is called equivalent Legendre polynomial (ELP). Several numerical examples serve to demonstrate the efficiency and accuracy of the proposed method. Based on 2D and 3D problems of linear elastostatics, the introduced method is further evaluated in the concept of the fictitious domain finite element methods.
DDC Class
510: Mathematik
More Funding Information
Deutsche Forschungsgemeinschaft (DFG)