Weak Galerkin Method for Electrical Impedance Tomography

TL;DR

This paper introduces a weak Galerkin method with bounded variation regularization for electrical impedance tomography, providing theoretical error estimates and numerical validation of its effectiveness and efficiency.

Contribution

It develops a novel weak Galerkin approach for EIT with convergence analysis and demonstrates its practical performance through numerical experiments.

Findings

Error estimates for the forward problem are established.

The weak Galerkin method converges for the inverse problem.

Numerical examples confirm the method's effectiveness.

Abstract

In this work, we propose and analyse a weak Galerkin method for the electrical impedance tomography based on a bounded variation regularization. We use the complete electrode model as the forward system that is approximated by a weak Galerkin method with lowest order. The error estimates are studied for the forward problem, which are used to establish the convergence of this weak Galerkin algorithm for the inverse problem. Numerical examples are presented to verify the effectiveness and efficiency of the weak Galerkin algorithm for the electrical impedance tomography.