In this paper, we introduce a new nonconforming finite element as a polynomial enrichment of the standard triangular linear element. Based on this new element, we propose an improvement of the triangular Shepard operator. We prove that the order of this new approximation operator is at least cubic. Numerical experiments demonstrate the accuracy of the proposed method.

On the improvement of the triangular Shepard method by non conformal polynomial elements

Dell'Accio F.;Di Tommaso F.;Nudo F.
2023-01-01

Abstract

In this paper, we introduce a new nonconforming finite element as a polynomial enrichment of the standard triangular linear element. Based on this new element, we propose an improvement of the triangular Shepard operator. We prove that the order of this new approximation operator is at least cubic. Numerical experiments demonstrate the accuracy of the proposed method.
Enriched finite element method
Nonconforming finite element
Scattered data interpolation
Triangular Shepard method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/341748
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