In order to avoid collapse of wells in oil fields, the use of steel casing has been a common technique throughout the last decades. However, the casing of a well with a steel pipe has some undesired effects. For instance, the assessment of electrical properties of the rock formation becomes more challenging, since the casing highly attenuates the electromagnetic fields. All these difficulties may be overcome by utilizing a novel numerical method based on a self-adaptive, goal-oriented hp-finite element method (FEM) that converges exponentially in terms of the quantity of interest vs. the problem size (as well as CPU time). The method is based on a purely numerical, highly accurate, and very reliable adaptive algorithm, which has been successfully applied to a variety of resistivity logging devices, including TCRT, induction, and normal/laterolog instruments. This methodology provides a guaranteed numerical error threshold below 0.1%, which allows for accurate simulation of meaningful physical effects in cased wells, such as invasion of water and/or anisotropy