A comparison between two solution techniques to solve the equations of glacially induced deformation of an elastic Earth

In this paper we compare two modeling frameworks within which we compute the Earth's elastic response to an external load. The main difference between the two frameworks lies in their capability to solve the partial differential equations (PDE) for a pre‐stressed elastic body, and especially how the term describing the pre‐stress advection is represented. Furthermore, the two frameworks differ in their applicability in the incompressible limit, the choice of the finite elements (FEs) used for the discretization, and the solution strategy for the arising algebraic problem. The two frameworks are denoted as Framework I and II. Framework I is confined to the features of a commercial FE package (ABAQUS), whereas Framework II is based on a code developed by the authors. The efficiency and accuracy of the two frameworks are compared via theoretical analysis and numerical experiments for two model problems in 2D and 3D. We find that the preconditioned iterative solution method used in Framework II is more efficient than the direct solver used in Framework I. Furthermore, we find that the solutions obtained from the two frameworks differ significantly for compressible solids. This is due to how the pre‐stress advection term is handled.