TY - JOUR
T1 - A Balanced Oversampling Finite Element Method for Elliptic Problems with Observational Boundary Data
AU - Chen , Zhiming
AU - Tuo , Rui
AU - Zhang , Wenlong
JO - Journal of Computational Mathematics
VL - 2
SP - 355
EP - 374
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1810-m2017-0168
UR - https://global-sci.org/intro/article_detail/jcm/14521.html
KW - Observational boundary data, Elliptic equation, Sub-Gaussian random variable.
AB - <p style="text-align: justify;">In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz $\psi_2$-norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included.</p>