Application Of The Hermite Interpolation FEM In Electrostatic Field

The Lagrange interpolation FEM is widely used in the electrostatic field, although it's calculation accuracy on potential is not high, especially the electric field accuracy is even worse. However, the Hermite interpolation FEM exactly make up for this defect. It is considered the node potential of the derivatives of coordinates as interpolation variable, so this finite element method can solve the electric field directly. High-precision interpolation brings high precision calculations. Meeting the same accuracy (particular the accuracy of electric field), Hermite interpolation FEM can save a lot of computing resources, and improve the computational efficiency.The difficulty of the Hermite interpolation FEM lies on boundary conditions and the convergence conditions of the interface among the different medium. In this paper, We use this interpolation to establish the finite element equation and deal with the boundary conditions and the interface conditions in medium. Using ANSYS to set up model and mesh grids, all the information of the grids are input into FORTRAN program to calculate. Comparing the Hermite interpolation with the Lagrange interpolation, it's proved that the former can greatly improve the calculation accuracy of the electric field in the same case of subdivision elements by two-dimensional electrostatic field calculation. By handing the boundary conditions, it's confirmed that Hermite interpolation FEM in the first boundary condition not only impose on the potential variables, but also impose the boundary along the tangent direction of the potential function derivative. However the second boundary conditions by normal derivative can not be impose through calculation. In the case of double-medium, the potential of the interface normal derivative is not continuous in the different medium. By modifying the variable or the equation, results can meet the convergence conditions in the interface. By calculation of two-dimensional multi-media electrostatic field, We verify the method of the convergence conditions of the interface correctness.