Semi-automatic mesh generation is a time-consuming and error-prone process. This is particularly true for engineering computations where the mesh requires varying levels of complexity. This paper studies two numerical models that produce converged solutions with the assistance of automatic adaptive mesh refinement, AMR. The studies illustrate how automatic adaptive mesh refinement can reduce modelling time as well as errors during the modelling process. The AMR solutions were performed using the SVFlux / FlexPDE software. The results are discussed in the contexts of the solutions published by Chapuis (2012). Chapuis (2012) analyzed the same problems while using user-controlled mesh design when performing the numerical solutions.