We construct a simple and robust finite volume discretization for linearized mechanics, Stokes and poromechanics, based only on co-located, cell-centered variables. The discretization has a minimal stencil, using only the two neighboring cells to a face to calculate numerical stresses and fluxes. We fully justify the method theoretically in terms of stability and convergence, both of which are robust in terms of the material parameters. Numerical experiments support the theoretical results, and shed light on grid families not explicitly treated by the theoretical results.

翻译：我们构建了一种基于同位、单元中心变量的简单稳健有限体积离散格式，适用于线性化力学、斯托克斯流及孔隙力学问题。该离散格式采用最小模板，仅利用相邻面的两个单元计算数值应力与通量。我们从稳定性和收敛性角度对该方法进行了完整的理论论证，两者均对材料参数具有鲁棒性。数值实验支持了理论结果，并揭示了理论结果未明确处理的网格族特性。