对流扩散方程的隐式全离散局部间断Galerkin方法  

Implicit Fully Discrete Local Discontinuous Galerkin Method for Convection Diffusion Equations

作　　者：赵思敏 宋灵宇[1] ZHAO Simin;SONG Lingyu(School of Science,Chang’an University,Xi’an Shaanxi 710061,China)

机构地区：[1]长安大学理学院,陕西西安710061

出　　处：《新疆大学学报（自然科学版中英文）》2024年第5期532-541,共10页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：中国博士后科学基金面上项目“三维颈动脉分叉处血管斑块生长自由边界问题的有限元方法及误差分析”(2022M722604);国家自然科学基金青年项目“颈动脉血管斑块生长自由边界问题稳态解的定性分析与数值模拟”(12101482);陕西省科技厅重点研发一般项目“肿瘤生长自由边界问题及预测系统研究”(2023-YBSF-372)。

摘　　要：研究了对流扩散方程的隐式全离散局部间断Galerkin方法的稳定性和误差分析.将三阶隐式Runge-Kutta时间离散和具有广义交替数值流通量的LDG方法相结合得到全离散LDG格式,通过广义交替数值流通量,建立数值解和辅助解内积之间的关系,证明了全离散LDG格式的无条件稳定,同时引入广义Gauss-Radau投影,通过投影的逼近性质和一些基本不等式建立了数值方法的最优误差估计,最后通过数值实验验证该方法理论分析的正确性.The stability and error analysis of the implicit fully discrete local discontinuous Galerkin method for convection diffusion equations are studied.The fully discrete LDG format is obtained by combining the third-order level implicit Runge-Kutta time discretization and the LDG method with generalized alternating numerical flux.Based on the generalized alternating numerical flux,the relationship between the inner product of the numerical solution and the auxiliary solution is established,and the unconditional stability of the fully discrete local discontinuous Galerkin format is demonstrated.At the same time,the generalized Gauss-Radau projection is introduced,and the optimal error estimate is established by the approximation properties of the projection and some basic inequalities,and finally the correctness of the theoretical analysis of the method is verified by numerical experiments.

关 键 词：对流扩散方程 局部间断Galerkin方法 隐式Runge-Kutta 广义交替流通量 

分 类 号：O241.82[理学—计算数学]