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.
