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Electrostatic problems are those that deal with the effects of electric charges at rest. For modern electron and microelectromechanical systems (MEMS), an accurate electrostatic analysis is both essential and indispensable. We know that if we use the conventional boundary element method for electrostatic problems that have singularity due to degenerate boundaries, the coincidence of the boundaries gives rise to a difficult, or ill-conditioned, problem. The coincidence is when different elements use the same nodes, but there is a free-edge between the elements. The dual boundary element method (DBEM) provides fast, accurate, and efficient solutions. We compare results between finite element method (FEM) and DBEM analyses to prove DBEM's superiority. Because model creation requires the most effort in electrical engineering practices, we strongly recommend DBEM for industrial applications.