Post Processing for the Vector Finite Element Method: from Edge to Nodal Values

Propose post processing methods for the edge finite element method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar values defined on the edges of the tetrahedra. Approach The new proposed techniques are based on a least squares formulation leading to a sparse matrix system to be solved. They are compared in terms of accuracy and CPU time on a FE formulation for open boundary – frequency domain problems. Findings 1 A significant improvement of vector values accuracy on the vertices of the tetrahedra is obtained compared to a classical approach with a very small additional computation time. Originality This work presents techniques allowing:- To obtain the values at the initial nodes of the mesh and not inside the tetrahedra- To take into account the discontinuity to the interface between two media of different electromagnetic properties