Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density (Advances in Applied Mathematics and Mechanics, 2024)
Numerical approximation of the Ericksen-Leslie system with variable density is considered in this paper. The spherical constraint condition of the orientationfield is preserved by using polar coordinates to reformulate the system. The equivalent new system is computationally cheaper because the vector function of the orientation field is replaced by a scalar function. An iteration penalty method is appliedto construct a numerical scheme so that stability is improved. We first prove that thescheme is uniquely solvable and unconditionally stable in energy. Then we show thatthis scheme is of first-order convergence rate by rigorous error estimation. Finally,some numerical simulations are performed to illustrate the accuracy and effectivenessof the scheme.