.png){kind=icon}
.png){kind=icon}
Return
Exponentially accurate least-squares spectral element method for modeling stationary heat diffusion in perforated domains
.png){kind=icon}
PRE
AI
A
M
M
DOI：10.1016/j.camwa.2026.04.016.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This paper presents a robust and exponentially accurate Least-Squares Spectral Element Method (LSQSEM) for modeling stationary heat diffusion in perforated domains. Such perforated heat diffusion models are central to the thermal analysis of Proton Exchange Membrane (PEM) fuel cells, where accurate prediction of temperature fields in perforated flow plates and membrane electrode assemblies is critical for thermal management, efficiency, and durability.The proposed LSQSEM minimizes a discrete functional incorporating residuals in the PDE, boundary conditions, and inter-element jumps in fractional Sobolev norms. We provide a comprehensive analysis including the least-squares formulation, stability estimates, numerical scheme, error estimates, and numerical results. We show that for analytic solutions the error between the exact and the computed solution decays exponentially as O(N5e−bW), where N denotes the number of elements and W denotes the polynomial order. The LSQSEM formulation gives rise to symmetric positive definite systems which are solved efficiently via preconditioned conjugate gradient method without the need to store the mass and stiffness matrices. Numerical experiments validate the exponential convergence and computational efficiency of the proposed method with periodic perforations and a combination of Dirichlet, Neumann and Robin boundary conditions.
Keywords:
Least-Squares Spectral Element Method
heat diffusion
perforated domains
exponential convergence
PEM fuel cells
Journal
C
IF:
2.5
Papers:
186
Citations:
0
View more organizations