State-of-the-art detectors are necessary to measure very tiny variations of gravity produced by spiraling neutron stars, merging black holes, moving tectonic plates. We are developing a superconducting gravity gradiometer and aim to achieve 0.1 mE Hz^{-1/2} in the frequency band of 0.1 mHz to 0.1 Hz. The superconducting test masses are levitated by a superconducting current-carrying monolayer pancake coil, which is one of the key components of the instrument. However, the nonlinear aspect of the magnetic field trapped between the test mass and the pancake coil imposes one of the main constraints to achieve that such low frequencies. In this paper, we investigated the causes of that nonlinearity by finite element method using COMSOL Multiphysics® simulation software. First, inductances were measured with an experimental setup where a gap spacing, created by a pancake coil and a niobium plate, could be adjustable. The inductances computed with a 2D axis-symmetric model satisfactorily agreed to the experimental data. Finally, we extensively studied several mechanisms for cancelling the nonlinearity of the inductance. A solenoid next to the pancake coil is the most effective and practical way to mitigate it. Furthermore, our approach can also be useful for those seeking a simple and effective model to study magnetostatic problems in a superconductor