Abstract
The 2D and 3D fully automatic hp adaptive Finite Element Method (FEM) codes generate a sequence of optimal hp refined meshes delivering exponential convergence rate of the numerical error with respect to the number of degrees of freedom (and CPU time). The optimal meshes are generated by performing a sequence of h or p refinements on the initial mesh. However, generation of optimal meshes in three dimensions is computationally expensive. We propose an algorithm for transferring of generated 2D optimal meshes into 3D meshes. The algorithm allows us to replace expensive 3D generation of optimal hp mesh by relatively inexpensive 2D generation of optimal meshes. The algorithm generates full revolution of the recorded optimal 2D mesh. The algorithm supports generation of either 3D axially symmetric meshes or non-axially symmetric tilted meshes. We apply that algorithm to perform a sequence of 3D DC borehole resistivity measurements simulations.