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Article Dans Une Revue Computers & Mathematics with Applications Année : 2024

New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite element

Francesco Dell'Accio
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Allal Guessab
Federico Nudo
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Résumé

In this paper, we introduce quadratic and cubic polynomial enrichments of the classical Crouzeix–Raviart finite element, with the aim of constructing accurate approximations in such enriched elements. To achieve this goal, we respectively add three and seven weighted line integrals as enriched degrees of freedom. For each case, we present a necessary and sufficient condition under which these augmented elements are well-defined. For illustration purposes, we then use a general approach to define two-parameter families of admissible degrees of freedom. Additionally, we provide explicit expressions for the associated basis functions and subsequently introduce new quadratic and cubic approximation operators based on the proposed admissible elements. The efficiency of the enriched methods is compared with that of the triangular Crouzeix–Raviart element. As expected, the numerical results exhibit a significant improvement, confirming the effectiveness of the developed enrichment strategy.
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Dates et versions

hal-04653419 , version 1 (18-07-2024)

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Francesco Dell'Accio, Allal Guessab, Federico Nudo. New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite element. Computers & Mathematics with Applications, 2024, 170, pp.204-212. ⟨10.1016/j.camwa.2024.06.019⟩. ⟨hal-04653419⟩

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