Stabilization of interconnected models with Nitsche's interface conditions using the two-grid approach: A finite element study

Abstract

In this paper, a stabilized Stokes–Stokes system with Nitsche's type interface conditions is presented. These conditions are commonly employed in many multi-physical fields, including fluid–fluid interaction, fluid–structure interaction, oceanographic modeling, and atmospheric forecasting. For multi-physical domain modeling purposes, Nitsche's interface conditions provide useful benefits over classical conditions via addressing the complicated nature of fluid phase interface mathematical modeling, phase boundary tracking, interface interactions, and mass and energy transportation. It is not easy to find analytical and numerical solutions for models with these characteristics. We use more accurate interface conditions to solve the fluid–fluid interaction model to accomplish this numerically. This is achieved by including new terms at the interface and decoupling the domain through the two-grid technique, which ultimately reduces the main issue into several smaller problems. Comparing this method to existing models, we find that it is computationally feasible because it uses less memory and operates with a coarse grid instead of a fine grid and thus improves convergence rates for complex and nonlinear problems. Furthermore, it shows mesh independence, supports potential parallelization, and is crucial for advanced multigrid techniques. The optimality of the error is confirmed both theoretically and numerically. The numerical experimental section validates the model through three types of numerical experiments.