Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes

IF 1 4区数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2023-10-04 DOI:10.1515/cmam-2023-0140

Shangyou Zhang

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Abstract

Abstract We construct three H-curl-curl finite elements. The P 2 P_{2} and P 3 P_{3} vector finite element spaces are both enriched by one common P 4 P_{4} bubble and their local degrees of freedom are 13 and 21, respectively. As there does not exist any P 1 P_{1} H-curl-curl conforming finite element, the P 1 P_{1} H-curl-curl nonconforming finite element is constructed with three additional P 4 P_{4} bubbles. Numerical tests are presented, confirming the conformity and the optimal order of convergence.

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三角网格上的三阶h -旋度有限元

摘要构造了三个h -旋度有限元。p2p_{2}和p3p_{3}矢量有限元空间均由一个共同的p4p_{4}泡丰富，其局部自由度分别为13和21。由于不存在p1p_ {1} H-curl-curl非一致性有限元，因此在p1p_ {1} H-curl-curl非一致性有限元中附加三个p4p_{4}气泡。通过数值试验，验证了算法的一致性和最优收敛顺序。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.