线性抛物方程的无网格法数值分析

doi:10.12677/aam.2026.157323

期刊菜单

线性抛物方程的无网格法数值分析
Numerical Analysis of Meshless Methods for Linear Parabolic Equations

DOI: 10.12677/aam.2026.157323, PDF, 科研立项经费支持
作者: 张涛：重庆科技大学数理科学学院应用数学系，重庆
关键词: 线性抛物方程；无单元Galerkin法；向后Euler法；Nitsche法；误差估计；Linear Parabolic Equation； Element-Free Galerkin Method； Backward Euler Method； Nitsche’s Method； Error Estimates

摘要: 针对混合边界的线性抛物方程，本文采用无单元Galerkin法进行空间离散，采用向后Euler法进行时间离散，并使用Nitsche法施加Dirichlet边界条件，获得了半离散误差估计和全离散误差估计，并通过数值算例验证了理论分析结果。

Abstract: In this paper, for linear parabolic equations with mixed boundary conditions, the element-free Galerkin method is employed for spatial discretization, the backward Euler method is used for temporal discretization, and Nitsche’s method is applied to impose the Dirichlet boundary conditions. The semi-discrete and fully discrete error estimates are obtained, and numerical examples are provided to validate the theoretical analysis results.

文章引用：张涛. 线性抛物方程的无网格法数值分析[J]. 应用数学进展, 2026, 15(7): 291-303. https://doi.org/10.12677/aam.2026.157323

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