Mixed formulation of a stationary seawater intrusion problem in confined aquifers

We consider a model mixing sharp and diffuse interface approaches for seawater intrusion phenomenon in confined aquifers. The problem consists of a strongly coupled system of partial differential equations of parabolic and elliptic types. The aim of this work is to introduce and analyze a new mixed formulation, obtained by writing the system into a matrix form and introducing a new variable sigma = R(u) backward difference u, representing the flux tensor of the primal variable u = (h,phi(f))(T). Here, h stands for the depth of salt/freshwater interface, phi(f), the hydraulic head of fresh water, and R(u) a symmetric and positive definite diffusion matrix. We show that the continuous problem as well as its mixed finite element approximation are well posed. We also provide optimal error estimates in L-2 -norm for both variables u and its associated flux sigma.

Automated summary

This paper introduces a mixed formulation for seawater intrusion phenomenon in confined aquifers. By writing the system into a matrix form and introducing a new variable sigma, the flux tensor of the primal variable u, the well-posedness of the continuous problem and its mixed finite element approximation are analyzed. Optimal error estimates in L-2-norm for both u and its associated flux sigma are also provided.