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PreprintCC BY-NC-ND 4.0arXiv

Optimal error estimates of sequential finite element method for nonlinear thermo-poroelasticity problems

  • Fan Chen
  • Changqing Lv
  • Chenguang Zhou
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Abstract

This study introduces and analyzes a three-step sequential decoupling algorithm designed to address nonlinear, fully coupled quasi-static thermo-poroelasticity systems incorporating convective transport. The finite element method is employed for spatial discretization and the backward Euler method for temporal discretization. The proposed sequential method has a higher computing efficiency than the fully implicit nonlinear numerical scheme, since it does not require any internal iterations. The well-posedness of the numerical solution is discussed by introducing a cut-off operator and the stability analysis of the algorithm is performed. Rigorous analysis yields optimal convergence order estimates for both spatial and temporal discretizations. In order to confirm the theoretical results and the effectiveness of the suggested approach, numerical experiments are finally carried out.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026optimal,
  title = {{Optimal error estimates of sequential finite element method for nonlinear thermo-poroelasticity problems}},
  author = {Fan Chen and Changqing Lv and Chenguang Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.29799},
  eprint = {2608.29799},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29799},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Optimal error estimates of sequential finite element method for nonlinear thermo-poroelasticity problems
AU  - Fan Chen
AU  - Changqing Lv
AU  - Chenguang Zhou
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2608.29799
UR  - https://arxiv.org/abs/2608.29799
AB  - This study introduces and analyzes a three-step sequential decoupling algorithm designed to address nonlinear, fully coupled quasi-static thermo-poroelasticity systems incorporating convective transport. The finite element method is employed for spatial discretization and the backward Euler method for temporal discretization. The proposed sequential method has a higher computing efficiency than the fully implicit nonlinear numerical scheme, since it does not require any internal iterations. The well-posedness of the numerical solution is discussed by introducing a cut-off operator and the stability analysis of the algorithm is performed. Rigorous analysis yields optimal convergence order estimates for both spatial and temporal discretizations. In order to confirm the theoretical results and the effectiveness of the suggested approach, numerical experiments are finally carried out.
ER  -