On the Convergence of Stochastic Finite Elements

DELAURENTIS, JOHN M. ; MOSHESH, IRENE

Sandia National Laboratories

关键词: Dimensions;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Stochastic Processes;    Hilbert Space;    Finite Element Method;   

DOI  :  10.2172/791887
RP-ID  :  SAND2001-3142
RP-ID  :  AC04-94AL85000
RP-ID  :  791887

美国|英语

来源: UNT Digital Library

【 摘 要 】

We investigate the rate of convergence of stochastic basis elements to the solution of a stochastic operator equation. As in deterministic finite elements, the solution may be approximately represented as the linear combination of basis elements. In the stochastic case, however, the solution belongs to a Hilbert space of functions defined on a cross product domain endowed with the product of a deterministic and probabilistic measure. We show that if the dimension of the stochastic space is n, and the desired accuracy is of order {var_epsilon}, the number of stochastic elements required to achieve this level of precision, in the Galerkin method, is on the order of | ln {var_epsilon} |{sup n}.