Viiteelementtiä

Viiteelementtiä is a Finnish term that translates to "finite element" in English. It refers to a fundamental concept in the field of numerical analysis, particularly in the finite element method (FEM). The finite element method is a powerful computational technique used to find approximate solutions to boundary value problems governed by partial differential equations.

In the context of FEM, a domain or structure is divided into a finite number of smaller, simpler subdomains called finite elements. These elements can be of various shapes, such as triangles, quadrilaterals, tetrahedrons, or hexahedrons, depending on the dimensionality of the problem. Within each element, the unknown function, which typically represents a physical quantity like displacement, temperature, or stress, is approximated using simple mathematical functions, often polynomials.

The behavior of the entire system is then determined by assembling the behavior of all individual finite elements. This assembly process involves relating the values of the unknown function at the nodes (corner points or boundaries) of the elements. By imposing continuity conditions and applying the governing physical laws, a system of algebraic equations is formulated. Solving this system of equations yields approximate values for the unknown function at the nodes, and from these nodal values, the behavior of the physical system can be inferred throughout the entire domain. The finite element method is widely used in engineering and physics for simulating phenomena such as structural analysis, heat transfer, fluid dynamics, and electromagnetics.