Hermite Cubic Elements are a type of finite element used in numerical analysis to approximate the solution of a partial differential equation. They are named after mathematician Charles Hermite and are based on the Hermite interpolation formula.
Hermite Cubic Elements have several advantages, including high accuracy and smoothness, good convergence properties, and the ability to handle complex geometry and boundary conditions. They are also efficient in terms of computational cost.
Hermite Cubic Elements are constructed by defining shape functions that satisfy the boundary conditions and are then combined with polynomial basis functions to approximate the solution. The coefficients of the shape functions are found by solving a system of linear equations.
Hermite Cubic Elements are commonly used for problems involving solid mechanics, heat transfer, fluid dynamics, and other physical phenomena that can be modeled by partial differential equations. They are particularly well-suited for problems with curved boundaries or discontinuous solutions.
While Hermite Cubic Elements have many advantages, they also have some limitations. They are more complex to implement than simpler finite elements, and may require a larger number of elements to achieve the same level of accuracy. Additionally, they may not perform well for problems with highly distorted elements or very high-order solutions.