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

• Main Author: Hrant A. Gevorgyan
• Format: Article
• Language: English
• Published: National Academy of Sciences of Belarus, State Scientific Institution “The Joint Institute of Mechanical Engineering" 2016-06-01
• Series: Механика машин, механизмов и материалов
• Subjects: finite and central differences; displacements scalar potential; scalar field; differential operators; gradient; divergence; laplacian; function derivative
• Online Access: http://mmmm.by/en/readers-en/archive-room-en?layout=edit&id=921

In the present article on the basis of earlier formulated planspatial problem of the finite elements method the concept of finite differences for the twodimensional 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 onedimensional environment is as degeneration the fundamental concept of mathematical analysis - the derivative of function of scalar argument.