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.

翻译：本文提出并分析了一种基于有界变差正则化的电阻抗成像弱伽辽金方法。我们采用完整电极模型作为正演系统，并用最低阶弱伽辽金方法对其进行近似。研究了正演问题的误差估计，并以此建立反问题弱伽辽金算法的收敛性。数值算例验证了该弱伽辽金算法在电阻抗成像中的有效性与高效性。