Simulation of rock salt dissolution and its impact on land subsidence

Extensive land subsidence can occur due to subsurface dissolution of evaporites such as halite and gypsum. This paper explores techniques to simulate the salt dissolution forming an intrastratal karst, which is embedded in a sequence of carbonates, marls, anhydrite and gypsum. A numerical model is developed to simulate laminar flow in a subhorizontal void, which corresponds to an opening intrastratal karst. The numerical model is based on the laminar steady-state Stokes flow equation, and the advection dispersion transport equation coupled with the dissolution equation. The flow equation is solved using the nonconforming Crouzeix-Raviart (CR) finite element approximation for the Stokes equation. For the transport equation, a combination between discontinuous Galerkin method and multipoint flux approximation method is proposed. The numerical effect of the dissolution is considered by using a dynamic mesh variation that increases the size of the mesh based on the amount of dissolved salt. The numerical method is applied to a 2D geological cross section representing a Horst and Graben structure in the Tabular Jura of northwestern Switzerland. The model simulates salt dissolution within the geological section and predicts the amount of vertical dissolution as an indicator of potential subsidence that could occur. Simulation results showed that the highest dissolution amount is observed near the normal fault zones, and, therefore, the highest subsidence rates are expected above normal fault zones

Local convergence of the FEM for the integral fractional Laplacian

We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm. Our estimates have the form of a local best approximation error plus a global error measured in a weaker norm

A General Superapproximation Result

A general superapproximation result is derived in this paper which is useful for the local/interior error analysis of finite element methods