Finite element modelling in implant dentistry

The use of numerical methods such as FEA has been adopted in solving complicated geometric problems, for which it is very difficult to achieve an analytical solution. FEA is a technique for obtaining a solution to a complex mechanics problem by dividing the problem domain into a collection of much smaller and simpler domains (elements) where field variables can be interpolated using shape functions. An overall approximated solution to the original problem is determined based on variational principles. In other words, FEA is a method whereby, instead of seeking a solution function for the entire domain, it formulates solution functions for each finite element and combines them properly to obtain a solution to the whole body. A mesh is needed in FEA to divide the whole domain into small elements. The process of creating the mesh, elements, their respective nodes, and defining boundary conditions is termed "discretization" of the problem domain. Since the components in a dental implant-bone system is an extremely complex geometry, FEA has been viewed as the most suitable tool to mathematically, model it by numerous scholars.