A conforming auxiliary space preconditioner for the mass conserving stress-yielding method

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Scientific computing

Background:

• Stokes equations are fundamental in fluid dynamics.
• Efficiently solving associated linear systems is crucial for simulations.
• Existing methods may lack scalability or robustness.

Purpose of the Study:

• To develop an efficient solution method for linear systems from MCS discretization of Stokes equations.
• To analyze the robustness of the method concerning polynomial degree.
• To demonstrate the approach's potential and implementation efficiency.

Main Methods:

• Static condensation to reduce the system size.
• An auxiliary space preconditioner for the velocity block.
• Analysis focused on low-order conforming Finite Element spaces.
• Numerical experiments to validate the approach.

Main Results:

• The proposed method efficiently solves the linear system.
• The auxiliary space preconditioner shows robustness across polynomial degrees.
• Numerical experiments confirm the approach's effectiveness and scalability.

Conclusions:

• The MCS discretization combined with static condensation and auxiliary space preconditioning offers an efficient solution for Stokes equations.
• The method is robust and scalable for various discretization polynomial degrees.
• This approach has significant potential for computational fluid dynamics applications.