摘要
新近提出的降阶单元的自适应有限元法,已在一系列初值问题和边值问题中取得成功,但尚缺乏与其他类似的自适应有限元法较为详细全面的对比分析。该文以一维非自伴随边值问题为模型问题,在最大模的度量下,同时考察现有的4种相类似的一维自适应有限元算法,进行对比计算和分析,总结参比方法的优劣。对比分析结果表明:作为自适应有限元分析方法,特别是从局部加密功能和性能来看,降阶单元原理简明、算法简单,在可靠、通用和计算效率等方面,均优于其他方法。
The recently proposed reduced element method for adaptive finite element(FE)analysis has been successfully applied to a series of initial and boundary value problems,yet there is a lack of detailed and comprehensive comparative analysis with other similar adaptive FE methods.By taking the one-dimensional nonself-adjoint boundary value problem as the model problem,four similar adaptive FE algorithms for the onedimensional problem are investigated with the maximum norm adopted to control errors.The comparative computation and analysis are carried out to identify the advantages and disadvantages of the four methods.The comparative analysis shows that as an adaptive FE analysis method,especially from the point of view of the local refinement capability,the reduced element method not only stands out for being simple and straightforward in theory and implementation,but also is superior to other methods in terms of reliability,versatility and efficiency.
作者
杨帅
袁驷
YANG Shuai;YUAN Si(Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Department of Civil Engineering,Tsinghua University,Beijing 100084,China)
出处
《工程力学》
北大核心
2025年第S1期1-8,共8页
Engineering Mechanics
基金
国家自然科学基金项目(51878383,51378293)。
关键词
降阶单元
边值问题
最大模
一维问题
自适应有限元
reduced element
boundary value problem
maximum norm
one-dimensional problem
adaptive FE
