EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis

YANG Shuai; YUAN Si

doi:10.21656/1000-0887.450036

Volume 46 Issue 1

Jan. 2025

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YANG Shuai, YUAN Si. EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis[J]. Applied Mathematics and Mechanics, 2025, 46(1): 1-11. doi: 10.21656/1000-0887.450036

Citation:

YANG Shuai, YUAN Si. EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis[J]. Applied Mathematics and Mechanics, 2025, 46(1): 1-11. doi: 10.21656/1000-0887.450036

Citation:

YANG Shuai, YUAN Si. EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis[J]. Applied Mathematics and Mechanics, 2025, 46(1): 1-11. doi: 10.21656/1000-0887.450036

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EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis

doi: 10.21656/1000-0887.450036

YANG Shuai^,,
YUAN Si

Key Laboratory of Civil Engineering Safety and Durability, Ministry of Education, Department of Civil Engineering, Tsinghua University, Beijing 100084, P.R.China

Funds:

The National Science Foundation of China(51878383；51378293)

Received Date: 2024-02-18
Rev Recd Date: 2024-05-08

Abstract

Abstract

For the elements of degree m(>1), simplified form solution u^* based on the element energy projection (EEP) method has at least 1-order higher accuracy than conventional finite element solution u^h.As a result, the EEP element, with simplified form EEP solution u^h in as the final solution, was proposed, and a corresponding adaptive finite element analysis strategy for EEP elements was developed. By means of the developed algorithm, the 1D 2-point boundary value problem was analyzed, and the computation results are in good agreement with theoretical solutions, verifying the effectiveness and reliability of the proposed adaptivity strategy. The theoretical study and numerical experiments show that, the proposed method provides an EEP element solution satisfying the preset error tolerances in the maximum norm with fewer elements and less adaptive steps compared to conventional finite elements.
- 1D problem,
- element energy projection (EEP),
- EEP element,
- adaptive finite element method

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References(21)

References

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