偏微分方程高效高精度数值方法研究  

STUDY OF HIGHLY EFFICIENT,EXTREMELY ACCURATE NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

作　　者：陈艳萍[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《华南师范大学学报（自然科学版）》2011年第4期1-9,共9页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10971074);广东省高等学校珠江学者岗位计划项目(2008);广东省高等学校人才引进专项资金项目

摘　　要：针对偏微分方程类型的最优控制问题、多孔介质渗流驱动问题、地下水流的非线性反应扩散方程、对流占有的对流扩散方程、Volterra积分微分方程等阐述混合有限元方法高精度后处理技术、具有超收敛性质的计算格式和高效自适应网格局部加密算法;扩张混合有限元快速收敛的两层网格算法;迎风差分格式的高效自适应移动网格算法;具有高精度的谱方法与谱元方法等多种现代的高效数值方法的有效性,介绍相关研究领域的前沿课题和最新进展.Numerical methods for partial differential equations（PDEs） are the main research area in computational mathematics.It includes finite difference method,finite element method,boundary element method and spectral method.In this paper,some contemporary topics and advanced development on numerical methods for PDEs will be introduced.The main focuses are on some applied science or engineering areas such as optimal control problems governed by partial differential equations,miscible displacement problems of one incompressible fluid by another in a porous medium,nonlinear reaction-diffusion equations,convection-dominated convection-diffusion problems,Volterra integral and differential equations.The basis of these new numerical techniques lies in the application of high accuracy,post-processing,super-convergence,two-grid method,adaptive mesh refinement,adaptive moving mesh method,and spectral method.

关 键 词：超收敛 后处理 局部加密 移动网格 两层网格 谱方法 

分 类 号：O241.82[理学—计算数学] O242.21[理学—数学]