Model adaptation for non-linear elliptic equations in mixed form: existence of solutions and numerical strategies

Depending on the physical and geometrical properties of a given porous medium, fluid flow can behave differently, going from slow Darcian regime to more complicated Brinkman or even Forchheimer regimes for high velocity. The main problem is determine where in medium one adequate than others. In order low-speed high-speed regions, this work proposes an adaptive strategy which based selecting appropriate constitutive law linking velocity pressure according threshold criterion magnitude itself. Both theoretical numerical aspects are considered investigated, showing potentiality proposed approach. From analytical viewpoint, we show existence weak solutions such model under reasonable hypotheses laws. To end, use variational approach identifying with minimizers underlying energy functional. propose one-dimensional algorithm tracks transition zone between low- regions. By running experiments using algorithm, illustrate some interesting behaviors our academic cases small networks intersecting fractures.