Numerical Reconstruction of Coefficients in Elliptic Equations Using Continuous Data Assimilation
Numerical Analysis
2025-10-07 v2 Numerical Analysis
Abstract
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet boundary condition and given interior observations of the solution. Using data assimilation, we derive approximated gradients of the error functional to update the reconstructed coefficients. New error estimates are provided for the spatially discretized reconstructions. Numerical examples are given to illustrate the effectiveness of the method and demonstrate the error estimates. The numerical results also show that the reconstruction is very robust to the errors in specific inputted coefficients.
Cite
@article{arxiv.2509.16954,
title = {Numerical Reconstruction of Coefficients in Elliptic Equations Using Continuous Data Assimilation},
author = {Peiran Zhang},
journal= {arXiv preprint arXiv:2509.16954},
year = {2025}
}