Fully Discrete Stabilized Mixed Finite Element Method Based On Two Local Gauss Integrations For The Polymer Gel Model

In this paper, we propose a fully discrete stabilized mixed finite element method based on two local Gauss integrations for a displacement-pressure model which describes swelling dynamics of polymer gels under mechanical constraints. Firstly, by introducing a new variable, we decouple the polymer gel model at each time into two subproblems-a Stokes-like problem and a diffusion problem, so we can reveal the underlying multiphysics process. Then, we propose the lowest equal-order stabilized mixed finite element method based on two local Gauss integrations to solve the new equations, also, we prove that the method is stable and give the error analysis. Finally, we use a numerical example to verify the theoretical results.