期刊
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
卷 10, 期 2, 页码 378-393出版社
UNIV BELGRADE, FAC ELECTRICAL ENGINEERING
DOI: 10.2298/AADM160610012B
关键词
Enriched finite element method; nonconforming finite element; the enriched Crouzeix-Raviart element; multivariate trapezoidal cubature formulas; error estimates
资金
- International Scientific Partnership Program (ISPP) at King Saud University (ISPP) [0028]
We provide a simple condition, which is both necessary and sufficient, that guarantees the existence of an enriched Crouzeix-Raviart element. Our main result shows that the latter can be easily expressed in terms of the approximation error in a multivariate generalized trapezoidal type cubature formula. Furthermore, we derive simple explicit formulas for its associated basis functions, and then prove how to use them to characterize all admissible added degrees of freedom, that generate well defined enriched Crouzeix-Raviart elements. We also show that the approximation error using the proposed enriched element can be written as the error of the (non-enriched) CrouzeixRaviart element plus a perturbation that depends on the enrichment function. Finally, we estimate the approximation error in L-2 norm, with explicit constants in both two and three dimensions. A complement to this result is also given for any dimension.
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