High-order structure-preserving approaches for constrained conservative or dissipative systems

Abstract

We propose a class of high-order schemes preserving original conservation/dissipation energy law and constraints for the constrained conservative/dissipative system. These schemes are efficient, i.e., only require solving linear system with constant coefficients at each time step, plus an algebraic optimization problem which consumes negligible cost. The proposed schemes are applied to conservative semiclassical nonlinear Schrödinger equation, as well as dissipative three-component ternary Cahn-Hilliard phase-field model. Some numerical experiments are conducted to validate applicability, effectiveness and accuracy of the proposed schemes.