A locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations
Abstract
We develop and analyze a locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations. The pressure, electric, magnetic, and displacement fields are discretized by the lowest-order nodal, edge, face, and Stokes-like virtual element spaces, respectively, so that the scheme works on general polyhedral meshes, while the temporal discretization is carried out by a backward Euler scheme. The locking phenomenon is overcome by defining the Stokes-like space on a refined mesh 𝒯̃h, on which we can construct an interpolation operator Is satisfying ÷(Isv)|K=ΠK0÷v, which renders the error estimates independent of the Lamé constant λ. Moreover, since the exact sequence curlVeh=Vfh,0 holds, the magnetic field is updated explicitly, reducing the four-field system to a three-field one and lowering the computational cost. Numerical experiments are provided to demonstrate the performance of the proposed method.
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BibTeX
@misc{huang2026lockingfree,
title = {{A locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations}},
author = {Jianguo Huang and Wenxuan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09646},
eprint = {2610.09646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09646},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations
AU - Jianguo Huang
AU - Wenxuan Wang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09646
UR - https://arxiv.org/abs/2610.09646
AB - We develop and analyze a locking-free virtual element method for the three-dimensional quasi-static electroporoelasticity equations. The pressure, electric, magnetic, and displacement fields are discretized by the lowest-order nodal, edge, face, and Stokes-like virtual element spaces, respectively, so that the scheme works on general polyhedral meshes, while the temporal discretization is carried out by a backward Euler scheme. The locking phenomenon is overcome by defining the Stokes-like space on a refined mesh 𝒯̃_h, on which we can construct an interpolation operator I_s satisfying ÷(I_sv)|_K=Π^K_0÷v, which renders the error estimates independent of the Lamé constant λ. Moreover, since the exact sequence curlV^e_h=V^f_h,0 holds, the magnetic field is updated explicitly, reducing the four-field system to a three-field one and lowering the computational cost. Numerical experiments are provided to demonstrate the performance of the proposed method.
ER -