One-Dimensional Finite Element Method for Inhomogeneous Electrostatic Potential and Field

In this paper, we propose a one-dimensional (1-D) finite element method (FEM) with fast construction of scalar basis functions and high solution accuracy in solving the electrostatic problems. Adopting the coordinate mapping to capture the basis function, the FEM can be implemented by the Gaussian integration. Compared with analytical solution, the computational errors from the 1-D FEM numerical solution will be less than 10
⁻¹⁰
once the computational boundary is given. As the computational grid is encrypted, the numerical accuracy can be well enhanced to satisfy the current industrial environment.