Fully Discrete Discontinuous Galerkin Numerical Scheme with Second-Order Temporal Accuracy for the Hydrodynamically Coupled Lipid Vesicle Model.

In this paper, for the highly nonlinear hydrodynamically coupled elastic bending energy model of vesicle membranes, based on the discontinuous Galerkin (DG) method for spatial discretization, a linear, decoupled, and second-order time-accurate numerical scheme is constructed. The scheme combines several efficient approaches, including the scalar auxiliary variable (SAV) method for the linearization of the nonlinear energy potential, the implicit-explicit (IMEX) discretization method for dealing with the nonlinear coupling terms, and the projection method for the Navier–Stokes equations. We also rigorously establish the energy stability and optimal error estimates, and also carry out several numerical examples to demonstrate the accuracy, stability, and efficiency of the proposed fully discrete DG scheme, numerically. [ABSTRACT FROM AUTHOR]