Convergent finite element methods for compressible barotropic Stokes systems
This work provides rigorous convergence guarantees for numerical methods in a specific class of fluid dynamics problems, which is incremental for the field of numerical analysis.
The paper proposes finite element methods for compressible barotropic Stokes systems and proves their convergence using higher integrability estimates, discrete effective viscous flux equations, and renormalized formulations.
We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete density, equations for the discrete effective viscous flux, and renormalized formulations of the numerical method for the density equation.