A discontinuous Galerkin pressure correction scheme for the incompressible Navier–Stokes equations: Stability and convergence
Rami Masri, Chen Liu, Béatrice Rivière
Abstract
A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier–Stokes equations is formulated and analyzed. We prove unconditional stability of the proposed scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. Numerical results verify the convergence rates.
Topics & Concepts
MathematicsConvergence (economics)CompressibilityGalerkin methodPressure-correction methodStability (learning theory)Discontinuous Galerkin methodNavier–Stokes equationsA priori and a posterioriMathematical analysisApplied mathematicsRate of convergenceScheme (mathematics)Numerical stabilityStokes problemNumerical analysisFinite element methodMechanicsPhysicsEconomic growthElectrical engineeringEpistemologyMachine learningChannel (broadcasting)Computer scienceEconomicsThermodynamicsEngineeringPhilosophyAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsNumerical methods for differential equations