Electrostatic field smooth finite element numerical algorithm based on finite element super-convergence

The invention discloses an electrostatic field smooth finite element numerical algorithm based on finite element super-convergence. The algorithm comprises the steps: inputting data, wherein the data is numerical data; according to the node numbers and the node coordinates, circulating all the nodes according to the sequence of the node numbers, and judging whether the node is an internal node or not; when the node is the internal node, determining a unit set near the reconstruction point, and calculating coordinates of a super-convergence point near the reconstruction point and an original gradient of the super-convergence point so as to calculate polynomial expansion and reconstruction gradients, the internal node being a common node of at least a preset number of units; and when the node is not the internal node, determining the unit set near the reconstruction point, and calculating the gradient of the reconstruction points in different units and the gradient average value of the reconstruction points. Th