On the improvement of the triangular Shepard method by nonconformal polynomial elements

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. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

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In this paper, a new nonconforming finite element is presented, which is a polynomial enrichment of the standard triangular linear element. Based on this new element, an improvement of the triangular Shepard operator is proposed. It is proven that the order of the new approximation operator is at least cubic. Numerical experiments verify the accuracy of the proposed method.