题    目：Energy-decaying ERK-SAV finite element methods for the time-dependent Ginzburg-Landau equations under the zero electric potential gauge

主讲人：姚昌辉  教授

单    位：郑州大学

时    间：2026年1月21日 16:00

地    点：九章学堂南楼C座302

摘    要：By the scalar auxiliary variable (SAV) approach and stabilization method, the                                  time-dependent Ginzburg-Landau equations under the zero electric potential gauge (also known as   the temporal gauge) are reformulated as an equivalent physical system that still inherits the energy-decaying property. And then, for the equivalent physical system, a class of linearized and extrapolated Runge-Kutta (ERK) finite element numerical schemes are constructed, which can achieve arbitrary  high-order accuracy in time.In order to demonstrate the feasibility of the numerical schemes, a             several of specific implementation algorithms are designed. Moreover, it is rigorously proved that the proposed numerical schemes unconditionally satisfy the modified energy-decaying law in the              discrete sense. Finally, the provided numerical tests verify the validity and correctness of the                  theoretical analysis. For comparative purposes, we additionally investigate experiments based on a   neural network framework, which also demonstrate the error accuracy, and the evolution results of  energy and maximum norm.