A New Class of Efficient SAV Schemes with Lagrange Multipliers for Dissipative Systems with Global Constraints

Abstract

In this paper, we develop a class of efficient and accurate numerical schemes for general dissipative systems with global constraints. The schemes are based on the relaxed generalized SAV approach and the Lagrange multiplier approach, and enjoy many advantages such as solving only one linear system with constant coefficients and one nonlinear algebraic system for the Lagrange multipliers. Besides, the schemes preserve global constraints and are unconditionally energy stable with a modified energy, which is equal to the original energy in most cases. We present applications of the R-GSAV/LM approach to a variety of problems to demonstrate its effectiveness and advantages compared with existing approaches.