A Balanced Oversampling Finite Element Method for Elliptic Problems with Observational Boundary Data
Year: 2020
Author: Zhiming Chen, Rui Tuo, Wenlong Zhang
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 355–374
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1810-m2017-0168
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 355–374
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Observational boundary data Elliptic equation Sub-Gaussian random variable.