Node Adaptive Finite Element Method Based On Hodge Decomposition For 2D Maxwell Equation

The efficient numerical method of Maxwell equation needs to satisfy the interface condition of electromagnetic field,so the finite element method of the electromagnetic field problem generally uses the edge finite element space.Compared with the traditional nodal element,the disadvantage of the edge element is that it has many degrees of freedom and the condition number of the linear system is poor.In this paper,a method based on Hodge decomposition is used to convert Maxwell equation into a standard elliptic boundary value problem,then use node element to solve the ellipse problem and then get the numerical solution of Maxwell equation.Because Hodge decomposition is used,non-physical numerical solutions are avoided in numerical solutions.We use SCR and PPR techniques to post-process the finite element numerical solution,which effectively improves the accuracy of the numerical solution,and establishes a reliable posterior error indicator and adaptive finite element method.Finally,four examples are given to verify the effectiveness and accuracy of the method.