标题： 关于应力辅助扩散问题的稳健虚拟元方法的后验误差分析 显示英文标题

标题： A posteriori error analysis of a robust virtual element method for stress-assisted diffusion problems

摘要： 我们研究并分析了残差型后验误差估计，用于二维和三维非线性应力辅助扩散问题的虚拟元离散化。 该模型问题涉及弹性方程与扩散方程在扰动鞍点形式下的双向耦合。 稳健的全局 inf-sup 条件和针对 $\mathbf{H}(\mathrm{div}, \Omega)$ 的 Helmholz 分解导致基于适当加权范数的可靠且高效的误差估计器，这些范数确保了参数稳健性。 后验误差分析使用了 Stokes 和边缘虚拟元空间的拟插值算子，并且完整地包含了这些算子及其三维估计的证明。 最后，我们在二维和三维中展示了数值实验，以证明所提出的误差估计器的最优性能。 显示英文摘要

摘要： We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between elasticity and diffusion equations in perturbed saddle-point form. A robust global inf-sup condition and Helmholtz decomposition for $\mathbf{H}(\mathrm{div}, \Omega)$ lead to a reliable and efficient error estimator based on appropriately weighted norms that ensure parameter robustness. The a posteriori error analysis uses quasi-interpolation operators for Stokes and edge virtual element spaces, and we include the proofs of such operators with estimates in 3D for completeness. Finally, we present numerical experiments in both 2D and 3D to demonstrate the optimal performance of the proposed error estimator.