非线性热孔隙弹性问题的序列有限元方法的最优误差估计
Optimal error estimates of sequential finite element method for nonlinear thermo-poroelasticity problems
- Zaozhuang University（枣庄大学）
- Beijing University of Technology（北京工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究针对含对流输运的非线性全耦合准静态热孔隙弹性系统，提出三步序列解耦算法，经理论分析获最优收敛阶，实验验证其效率与有效性优于全隐式格式。
AI中文摘要：
本研究引入并分析了一种三步序列解耦算法，用于求解含对流输运的非线性、全耦合准静态热孔隙弹性系统。空间离散采用有限元方法，时间离散采用向后欧拉方法。所提序列方法比全隐式非线性数值格式计算效率更高，因为它无需任何内部迭代。通过引入截断算子讨论了数值解的适定性，并对算法进行了稳定性分析。严格分析得到了空间和时间离散的最优收敛阶估计。最后开展数值实验以验证理论结果和所提方法的有效性。
英文摘要：
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.
