  In this paper we study newly developed methods for linear elasticity on
polyhedral meshes. Our emphasis is on applications of the methods to geological
models. Models of subsurface, and in particular sedimentary rocks, naturally
lead to general polyhedral meshes. Numerical methods which can directly handle
such representation are highly desirable. Many of the numerical challenges in
simulation of subsurface applications come from the lack of robustness and
accuracy of numerical methods in the case of highly distorted grids. In this
paper we investigate and compare the Multi-Point Stress Approximation (MPSA)
and the Virtual Element Method (VEM) with regards to grid features that are
frequently seen in geological models and likely to lead to a lack of accuracy
of the methods. In particular we look how the methods perform near the
incompressible limit. This work shows that both methods are promising for
flexible modeling of subsurface mechanics.
