A Cfl-Free Lagrangian Discontinuous Galerkin Method for the Oseen Equations

Abstract

ACFL-freeLagrangiandiscontinuousGalerkinmethodisstudiedforsolvingthetime-dependentOseen equations. It is proved that the fully discrete velocity is bounded in L∞and H1norms without anyCFL time-step restriction by using the temporal-spatial error split schemes. Error estimates of the veloc-ity and pressure in L2-norm are derived, respectively with the bound. The theoretical study on CFL freescheme is given by the process of numerical analysis for the Lagrangian methods in the DG framework.Numerical results are performed to illustrate the error accuracy and stability.

Keywords: discontinuous Galerkin methods； Lagrangian schemes；Oseen equations； stability； error estimates； numerical methods.