四川大学学报（自然科学版）2026，Vol.63Issue(1)：91-99,9.DOI:10.19907/j.0490-6756.240124
对流扩散方程的隐显龙格库塔间断有限元法
An implicit-explicit Runge-Kutta discontinuous Galerkin method for advection-diffusion equations
摘要
Abstract
In this paper,an implicit-explicit Runge-Kutta discontinuous Galerkin method is proposed for the advection-diffusion equation.In the method,a two-stage Runge-Kutta scheme is employed for the temporal discretization,a discontinuous Galerkin method is employed for the spatial discretization.Specifically,for the temporal discretization,an explicit two-stage Runge-Kutta scheme is used to the convection term as well as a diagonally implicit two-stage Runge-Kutta scheme is used to the diffusion term.For the spatial discretization,the discontinuous Galerkin method with upwinding is adopted for the advection term as well as the symmetric interior penalty discontinuous Galerkin method is adopted for the diffusion term.Rigorous error analysis and quasi-optimal error estimate are derived.Numerical examples confirm the superior performance of the method in the advection-dominated case of the advection-diffusion equation.关键词
对流扩散方程/隐显龙格库塔法/间断有限元法/对流占优Key words
convection-diffusion equation/implicit-explicit Runge-Kutta method/discontinuous Galerkin method/advection-dominated分类
数理科学引用本文复制引用
卿舒文,王璐,冯民富..对流扩散方程的隐显龙格库塔间断有限元法[J].四川大学学报（自然科学版）,2026,63(1):91-99,9.基金项目
国家自然科学基金(11971337) （11971337）
