A finite element method for elliptic problems with observational boundary data
Numerical Analysis
2017-02-20 v1
Abstract
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz 2- norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included.
Cite
@article{arxiv.1702.05188,
title = {A finite element method for elliptic problems with observational boundary data},
author = {Zhiming Chen and Rui Tuo and Wenlong Zhang},
journal= {arXiv preprint arXiv:1702.05188},
year = {2017}
}