The unique solvability analysis and error estimate of the Lagrange multiplier approach for gradient flows is theoretically analyzed. We identify a necessary and sufficient condition that has to be satisfied for the nonlinear algebraic equation arising from the original Lagrange multiplier approach to admit a unique solution in the neighborhood of its exact solution. In turn, a modified Lagrange multiplier approach is proposed so that the computation can continue even if the aforementioned condition is not satisfied. Using Cahn-Hilliard equation as an example, we rigorously establish the unique solvability analysis and optimal error estimates of a second-order Lagrange multiplier scheme assuming this condition and that the time step size is sufficiently small. 

王成教授, 1993年本科毕业于中国科技大学, 2000年在美国坦普尔大学获博士学位, 2000-2003年在美国印尼安纳大学从事博士后研究, 2003-2008年在美国田纳西大学任助理教授, 2008-2012年在美国麻省大学达特茅斯分校仟助理教授, 2012年晋升为副教授, 2019年晋升为教授。主要研究领域是应用数学与计算数学, 包括数值分析、偏微分方程、流体力学、计算电磁学等, 目前已在Journal of Computational Physics, SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik 等期刊上发表论文 120 余篇。