Error estimation and adaptive meshing in 3D electrostatic and magnetostatic problems

A local error estimation and adaptive meshing method developed by some of the authors for finite element analysis of 2D electrostatic and magnetostatic problems is now extended to 3D problems. The problems are formulated in terms of scalar potentials and discretized on a tetrahedral mesh using linear shape functions. Local error is estimated by approximately solving an independent differential problem in each tetrahedral element. The elements selected for refinement are subdivided by adding nodes inside the element, or along an edge, depending on their geometrical quality factor.