A novel error analysis of nonconforming finite element for the clamped Kirchhoff plate with elastic unilateral obstacle

Lifang Pei; Man Zhang; Meng Li; Lifang Pei; Man Zhang; Meng Li

doi:10.3934/nhm.2023050

Networks and Heterogeneous Media

2023, Volume 18, Issue 3: 1178-1189. doi: 10.3934/nhm.2023050

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A novel error analysis of nonconforming finite element for the clamped Kirchhoff plate with elastic unilateral obstacle

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P.R China

Received: 18 December 2022 Revised: 26 February 2023 Accepted: 09 March 2023 Published: 06 April 2023

A nonconforming finite element method (FEM) is proposed and analyzed for the clamped thin elastic Kirchhoff plate unilaterally constrained by an elastic obstacle. The discrete scheme is constructed by using the strongly discontinuous Bergan's energy-orthogonal plate element, which has simple degrees of freedom and about 25 percent fewer global dimension than that of the famous triangular Morley element. A novel error analysis is presented to overcome the difficulties caused by the strong discontinuity and derive the optimal estimate. Numerical experiments are carried out to verify the theoretical analysis.
- elastic obstacle,
- kirchhoff plate,
- nonconforming FEM,
- Bergan's element,
- optimal error estimate
Citation: Lifang Pei, Man Zhang, Meng Li. A novel error analysis of nonconforming finite element for the clamped Kirchhoff plate with elastic unilateral obstacle[J]. Networks and Heterogeneous Media, 2023, 18(3): 1178-1189. doi: 10.3934/nhm.2023050

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Abstract

A nonconforming finite element method (FEM) is proposed and analyzed for the clamped thin elastic Kirchhoff plate unilaterally constrained by an elastic obstacle. The discrete scheme is constructed by using the strongly discontinuous Bergan's energy-orthogonal plate element, which has simple degrees of freedom and about 25 percent fewer global dimension than that of the famous triangular Morley element. A novel error analysis is presented to overcome the difficulties caused by the strong discontinuity and derive the optimal estimate. Numerical experiments are carried out to verify the theoretical analysis.

References

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