This review paper addresses the development of numerical modeling of electromagnetic fields in geophysics with a focus on recent finite element simulation. It discusses ways of estimating errors of our solutions for a perfectly matched modeling domain and the problems that arise from its insufficient representation. After a brief outline of early methods and modeling approaches, the paper mainly discusses the capabilities of the finite element method formulated on unstructured grids and the advantages of local h-refinement allowing for both a flexible and largely accurate representation of the geometries of the multi-scale geomaterial and an accurate evaluation of the underlying functions representing the physical fields. In summary, the accuracy of the solution depends on the geometric mapping, the choice of the mathematical model, and the spatial discretization. Although the available error estimators do not necessarily provide reliable error bounds for our complex geomodels, they are still useful to guide grid refinement. Therefore, an overview of the most common a posteriori error estimators is given. It will be shown that the sensitivity is the most important function in both guiding the geometric mapping and the local refinement.

本文讨论了地球物理学中电磁场数值模拟的发展，重点关注最近的有限元模拟。它讨论了估计我们的解决方案对于完美匹配的建模域的错误的方法以及由于其不充分的表示而产生的问题。在简要概述了早期方法和建模方法之后，本文主要讨论了在非结构化网格上制定的有限元方法的功能以及局部 h 细化的优点，允许灵活且大致准确地表示多网格的几何形状。缩放地质材料并准确评估代表物理场的基本功能。综上所述，求解的精度取决于几何映射、数学模型的选择以及空间离散化。尽管可用的误差估计器不一定为我们的复杂地理模型提供可靠的误差范围，但它们对于指导网格细化仍然有用。因此，给出了最常见的后验误差估计器的概述。将表明，灵敏度是指导几何映射和局部细化的最重要函数。