Abstract
This analysis will assess the performance of the Finite Element Method applied to a system of concentric and eccentric cylindrical conductors possessing physically realistic boundary conditions in conjunction with simple and severe geometries. The electrostatic potential, electric field, and capacitance will be computationally determined to judge the accuracy between uniform and fixed mesh refinement (FMR) discretizations possessing similar element counts. It is concluded that use of FMR is beneficial in circumstances where the solution to the system under study varies rapidly in a portion of the domain, or where the geometry is severe enough that it affects mesh quality. Application of FMR to a concentric cylindrical conductor system reveals that it reduces the overall absolute error in the electrostatic potential by a factor of two when compared to the uniform mesh. In the case of an eccentric cylindrical conductor system, the absolute error is improved upon by a factor of ∼2 and the relative error around the interior conductor by ∼2. Lastly, the capacitance produced with both meshes often yield relative errors < 1% when compared to the analytical solution except in cases of severe geometric boundaries where FMR improves on the uniform mesh result by a factor of ∼2.