An Interpretation of the Geometric Meaning of the Finite Difference and the Function Derivative through the Use of the Finite Element Method Tools

Abstract

In the present article on the basis of earlier formulated plan spatial problem of the finite elements method the concept of finite differences for the two dimensional continuous environment is developed. According to the indicated development, are formulated the operators of the gradient and Laplacian of the scalar field for whom in the case of the one dimensional environment is as degeneration the fundamental concept of mathematical analysis - the derivative of function of scalar argument.

Keywords

• finite and central differences
• displacements scalar potential
• scalar field
• differential operators
• gradient
• divergence
• laplacian
• function derivative