High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

作     者：Wei Zheng Yan Xu Wei Zheng;Yan Xu

作者机构：School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei230026AnhuiChina 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2024年第6卷第1期

页      面：372-398页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the NSFC grant 12071455 

主　　题：Chemotaxis models Local discontinuous Galerkin(LDG)scheme Convex splitting method Variant energy quadratization method Scalar auxiliary variable method Spectral deferred correction method 

摘      要：In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent *** use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the *** semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction *** bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order *** overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time *** bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton *** numerical experiments illustrate the high-order accuracy and the effect of bound preserving.