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
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。
Abstract: 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.
文章引用：罗宏. 二维非线性对流扩散问题的Galerkin方法[J]. 应用数学进展, 2024, 13(8): 3585-3591. https://doi.org/10.12677/AAM.2024.138341

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