The ecient numerical method of Maxwells equation needs to satisfy the interface condition of electromagnetic eld, so the nite element method of the electromagnetic eld problem generally uses the edge nite 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 Maxwells equation into a standard elliptic boundary value problem, then use node element to solve the ellipse problem and then get the numerical solution of Maxwells equation. Because Hodge decomposition is used, non-physical numerical solutions are avoided in numerical solutions. This paper uses Superior Capsular Reconstruction (SCR) and Polynomial Preserving Recovery (PPR) techniques to post-process the nite element numerical solution, which eectively improves the accuracy of the numerical solution, and establishes a reliable posterior error indicator and adaptive nite element method. Finally, four examples are given to verify the eectiveness and accuracy of the method.
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