*2.4. Numerical Finite Element (FE) Solution and Convergence*

The numerical schemes were implemented in the ANSYS software package (version 11.0, ANSYS Inc., Canonsburg, PA, USA), by the finite element method using quadrangular plane finite elements with Lagrangian approximation and two degrees of freedom at each node. The basic procedures for constructing FE models are based on the use of the Galerkin method procedure with the choice of basic functions with a compact support by the finite element method.

The analysis of the convergence of the results of the numerical solution of the problem of contact interaction of a pair of teeth with and without a protective mouthguard from the degree of discretization of the system was carried out in an earlier paper [21]. It was found that a finite element mesh with a gradient concentration of elements to the contact zones provides an optimal solution to the problem in terms of accuracy and computation time: the maximum element size is 0.25 mm, the minimum element size is approximately 4 times less than the maximum one. The finite element subdivision of the biomechanical units considered in this work was performed similarly to the previously selected mesh.
