As opposed to the standard discrete system, the more general Finite Element method utilizes what?

As opposed to the standard discrete system, the more general Finite Element method utilizes what?

• A. Exact Solutions
• B. Numerical Integration
• C. Approximations
• D. Discretization

Answer: (C)

The finite element method builds the solution from simple, adjustable functions defined on small elements, so the overall result is an approximation to the true field. Instead of solving for an exact continuum solution, FEM represents the unknown quantities with interpolation (shape) functions within each element and assembles many local equations into a finite set for those coefficients. This is why the method yields an approximate solution: the accuracy depends on the order of the interpolation and how finely the domain is meshed. Numerical integration is a common tool used to compute the element equations, and discretizing the domain into elements is essential, but the defining feature is using approximations to represent the solution rather than solving it exactly.

The finite element method builds the solution from simple, adjustable functions defined on small elements, so the overall result is an approximation to the true field. Instead of solving for an exact continuum solution, FEM represents the unknown quantities with interpolation (shape) functions within each element and assembles many local equations into a finite set for those coefficients. This is why the method yields an approximate solution: the accuracy depends on the order of the interpolation and how finely the domain is meshed. Numerical integration is a common tool used to compute the element equations, and discretizing the domain into elements is essential, but the defining feature is using approximations to represent the solution rather than solving it exactly.