Discretization of Finite Element Analysis

Introduction

The method of converting continuous model to discrete counterparts is referred as discretization. This discretization helps in numerical mathematical method of evaluation. Discretization is referred as quantization in the digital computer field. Discretization of finite element analysis method schematic representation is as follows.

• Choosing a basis
• Small support of the basis
• Matrix form of the problem
• General form of the finite element method

Choosing a basis

Finite element method refers to any of the domain triangle. Curved domains shall be replaced by curved primitive. This refers elements as curvilinear. The element shall be piecewise quadratic or piecewise linear and or even piecewise polynomial. This method does not limit with triangle; it can also be applied to quadrilateral sub domains. Polynomials define curvilinear elements and non polynomial shape like circle or ellipse.

Methods like hp FEM and spectral FEM are used for polynomial analysis basis. Techniques of mesh adaptivity are

• h adaptivity
• p adaptivity
• r adaptivity
• hp adaptivity

General form of finite element method

Grid and basic functions have to be selected. Grid can be triangle, square or curvilinear polygons. Basis function can be piece wise polynomial function or piece wise linear function. Basis function smoothness and finite dimensional space with respect to infinite dimensional space has to be considered.

Questions:

• What is discretization?
• How to choose a basis for discretization?
• What is the application of discretization of finite element analysis method?