二维非线性对流扩散问题的Galerkin方法  

Galerkin’s Method for Two-Dimensional Nonlinear Convection-Diffusion Problems

作　　者：罗宏 

机构地区：[1]长沙理工大学数学与统计学院,湖南 长沙

出　　处：《应用数学进展》2024年第8期3585-3591,共7页Advances in Applied Mathematics

摘　　要：本文研究了一种具有狄利克雷边界的二维非线性对流扩散方程的Galerkin有限元法。 基于一 种具有两个内置参数的特殊变分形式,提出了半离散Galerkin有限元格式,并且理论上导出 了半离散Galerkin有限元格式H1范数下最优误差估计。 给出两个数值实验,时间方向分别采 用Grank-Nicolson格式和向后欧拉格式进行离散,验证理论分析结果。In this paper, a Galerkin finite element method for a two-dimensional nonlinear convection-diffusion equation with a Delicacy boundary is investigated. Based on a special variational form with two built-in parameters, a semi-discrete Galerkin finite element format is proposed, and the optimal error estimate in the H1 paradigm of the semi-discrete Galerkin finite element format is derived theoretically. Two numerical experiments are given, where the time direction is discretised in Grank-Nicolson for- mat and backward Eulerian format, respectively, to validate the theoretical analysis.

关 键 词：非线性对流扩散方程 GALERKIN有限元法 误差估计 

分 类 号：O24[理学—计算数学]