Finitemetoden

Finitemetoden, often referred to as the Finite Element Method (FEM), is a powerful numerical technique used to approximate solutions to partial differential equations (PDEs) and integral equations. Its fundamental principle involves discretizing a complex problem domain into smaller, simpler, interconnected 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 finite element, the unknown solution is approximated by a simple function, typically a polynomial. The behavior of these local approximations is then assembled into a global system of algebraic equations that represents the entire problem domain. This system is then solved using standard numerical methods to obtain approximate values of the solution at specific points, known as nodes, which are located at the boundaries of the elements.

The accuracy of the FEM solution generally improves as the number of finite elements increases or as the complexity of the approximating functions within each element is enhanced. This method finds widespread applications in various engineering and scientific disciplines, including structural analysis, heat transfer, fluid dynamics, electromagnetics, and acoustics. Its ability to handle complex geometries and boundary conditions makes it an indispensable tool for simulating and analyzing physical phenomena.