[2022/04/17] High-order and energy-stable numerical methods for the gradient flows

Title : High-order and energy-stable numerical methods for the gradient flows

Time : Apr. 17 (Mon), 2:00 pm - 3:00 pm

Place : 32356 SKKU, Suwon

Speaker : Prof. Jaemin Shin (Chungbuk University)

Abstract :

This presentation will introduce high-order and energy-stable numerical methods for gradient flows. The governing equations for gradient flows have a property of energy evolution based on a specific inner product space. Therefore, numerical methods are energy-stable if they inherit this property. Additionally, a high-order accuracy prefers to obtain an accurate numerical solution. To achieve a high-order scheme while maintaining energy stability, we have designed several numerical methods, including the convex splitting Runge-Kutta method, convex Runge-Kutta method, energy quadratization Runge-Kutta method, and successive multi-stage method.