A second order accurate, energy stable numerical scheme for the thin film model without slope selection is studied.  The key difficulty is associated with the complicated form of the nonlinear term, which corresponds to a non-convex, non-concave energy functional. In turn, a direct application of a linear splitting approach leads to a first order accurate numerical scheme with energy stability. To improve the temporal accuracy while preserving the energy stability, one could apply either the implicit or explicit treatment for the nonlinear term. In the explicit approach, we need to add a Doulas-Dupont type regularization term to ensure the energy stability at a theoretical level. In addition, a great simplification is enjoyed in the computation effort for the resulting scheme, due to the fact that only a constant-coefficient linear solver is needed at each time step. Some numerical results are also presented.    

Cheng Wang received his Ph.D (under Jian-Guo Liu) at Temple University, USA, in 2000. Afterward, he spent 3 years at Indiana University as a postdoc, with Roger Temam and Shouhong Wang as his postdoc mentors. In 2003-2008, he was a tenure-track assistant professor at University of Tennessee. In 2008, he moved to University of Massachusetts dartmouth; right now he is an associate professor there. His research area is applied mathematics, including numerical analysis, partial differential equations, fluid mechanics, computational electro-magnetics, material sciences, etc; he has had over 40 peer-reviewed articles at different scientific journals.