%0 Journal Article
%T 二维非线性对流扩散问题的Galerkin方法<br>Galerkin’s Method for Two-Dimensional Nonlinear Convection-Diffusion Problems
%A 罗宏
%J Advances in Applied Mathematics
%P 3585-3591
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/AAM.2024.138341
%X 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H<sup>1</sup>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。<br />
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 H<sup>1</sup> 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.
%K 非线性对流扩散方程，Galerkin有限元法，误差估计<br>Nonlinear Convection-Diffusion Equation
%K Galerkin Finite Element Method
%K Error Estimation
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=92668