The Local Discontinuous Galerkin And Scalar Auxiliary Variable Methods For The Swift-Hohenberg Equation

The main content of this paper is the local discontinuous Galerkin(LDG)method and scalar auxiliary variable(SAV)methods for the Swift-Hohenberg equation.For spatial discretization,we develop an LDG method and prove the energy stability of the semi-discrete LDG method.For temporal discretization,the Swift-Honhenberg equation is a fourth order nonlinear partial differential equation,which leads to the severe time step restriction(?)of explicit time stepping methods to maintain stability.Due to this,we introduce first-and second-order SAV methods and prove the corresponding unconditional energy stabilities.Finally,some numerical examples are given to verify the theoretical results and the efficiency of the proposed numerical methods.