Abstract
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 σ = R(u)∇u, representing the flux tensor of the primal variable u = (h,Φf)T. Here, h stands for the depth of salt/freshwater interface, Φf, 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 L2 −norm for both variables u and its associated flux σ.
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Slimani, S., Farhloul, M., Medarhri, I. et al. Mixed formulation of a stationary seawater intrusion problem in confined aquifers. Numer Algor 91, 651–669 (2022). https://doi.org/10.1007/s11075-022-01277-z
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DOI: https://doi.org/10.1007/s11075-022-01277-z