基于SPR的误差评估与回归场函数选择  

An error estimation based on SPR and selecting of recovered field function

作　　者：邵琪[1,2] 唐小微[1,2] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024 [2]大连理工大学土木工程学院岩土工程研究所,辽宁大连116024

出　　处：《大连理工大学学报》2013年第2期234-240,共7页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(51078062);“九七三”国家重点基础研究发展计划资助项目(2011CB013605-2)

摘　　要：有限元数值计算方法作为一种近似计算方法现已广泛应用于工程设计和研究中,当面对复杂问题需要获得更细致、更精确解的时候,就必须利用合理的误差评估甄别有限元的解并改进.因此,基于超收敛单元片回归/恢复(SPR)方法,分别采用一阶线性、双线性和二阶非线性多项式构造回归场函数进行误差评估,通过不同网格划分的算例验证了网格疏密程度与平均相对误差的关系,并将各回归场函数的评估结果与解析解结果进行比较,证明了双线性回归场函数不仅可用于三节点三角形单元,且对于粗糙网格比线性回归场的评估更精准.Finite element method （FEM） is widely applied to the design and study of engineering as an approximate numerical method. However, it is necessary to estimate errors of FEM solutions and improve them when facin on superconvergent patc g h complicated problems which need more accurate results. Therefore, based recovery （SPR） method, the recovered fields of linear, bilinear and nonlinear polynomial are used for error estimation. The relationship between average relative errors and density of meshes is verified, and due to the comparison between recovered results and analytic results, the bilinear recovered field function is proved to be suitable for 3-nodes triangular elements, and a more accurate estimation result can also be gained in the coarse mesh than the linear recovered field function.

关 键 词：有限元法 误差评估 SPR 应力 应变回归场 三角形单元 

分 类 号：TU435[建筑科学—岩土工程]