Methods to Solve Complex PDEs

• Discretization Methods: FEM / FDM / FVM / BEM / High Resolution Schemes
• FEM involves more complexity. It is generally used in multiphysics, electromagnetic, structural and quantum analysis due its higher accuracy.
• Difficulty wise: FDM < FVM < FEM

CFD Specific

• Vortex Methods (for incompressible Navier-Stokes equations), Lattice Boltzmann Method
• FVM is more commonly used in CFD. It discretizes PDEs to Algebraic Equations.