Transient heat transfer analysis of orthotropic materials considering phase change process based on element-free Galerkin method

Zhang, Jianping; Shen, Yang; Hu, Huiyao; Gong, Shengrong; Wu, Shuying; Wang, Zhiqi; Huang, Jian

doi:10.1016/j.icheatmasstransfer.2021.105295

Cited by 9 publications

(2 citation statements)

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“…In addition to choosing the interpolation-type MLS methods, some mandatory methods, such as the Lagrange multiplier method [ 3 , 4 , 13 ], Nitsche method [ 22 , 23 ] and penalty method [ 3 , 4 , 24 , 25 , 26 , 27 , 28 ] are desirable in practical applications. The important feature of these methods is that they can straightforwardly use the non-interpolating trial and test functions by modifying the traditional weak form.…”

Section: Introductionmentioning

confidence: 99%

“…In the context of the EFG method, many papers are devoted to penalty-based error analysis for elliptic problems [ 24 , 25 ], parabolic problems [ 26 , 28 ] and contact problems [ 27 ]. To the authors’ knowledge, for Stokes problems, a priori errors of the meshless penalty method have not been explained, and numerical analysis with a penalty factor has not been presented either.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems

Zhang

2022

Entropy

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The element-free Galerkin (EFG) method with penalty for Stokes problems is proposed and analyzed in this work. A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. Based on a feasible assumption, it is proved that there is a unique weak solution in the modified weak form of penalized Stokes problems. Then, the error bounds with the penalty factor for the EFG discretization are derived, which provide a rationale for choosing an efficient penalty factor. Numerical examples are given to confirm the theoretical results.

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