Comparison of Fist-Order Finite Difference and Finite Element Alogorithms for the Analysis of Magnetic Fields. Part I: Theoretical Analsyis

Finite difference and finite element methods are investigated as applied to Laplace and Poisson linear equations in two dimensions. The comparative analysis concentrates on first-order square, rectangular, triangular and polar algorithms which are characteristic to each method. The results are found to be independent of the method used to establish the matrix equations but dependent upon the choice of grid systems employed to discretize the problem. It is found that for special cases the solutions are also independent of the type and structure of the grid systems used.