A rectangular higher order edge element is a type of finite element used in the finite element method for numerical analysis. It is a higher order element, meaning it has a higher degree of polynomial interpolation, and it is designed specifically for modeling problems with a rectangular geometry and higher order continuity along the element edges.
A rectangular higher order edge element differs from a standard rectangular element in that it has a higher degree of polynomial interpolation along the element edges. This allows for a more accurate representation of curved or irregular boundaries, as well as smoother solutions.
The advantages of using a rectangular higher order edge element include higher accuracy and smoother solutions compared to standard rectangular elements. It also allows for more flexibility in modeling complex geometries and can reduce the overall number of elements needed in a finite element analysis.
The rectangular higher order edge element is commonly used in structural mechanics, particularly for problems involving curved or irregular boundaries. It is also used in fluid mechanics for modeling flows over complex geometries, and in electromagnetics for analyzing devices with curved boundaries.
In the finite element method, the rectangular higher order edge element is defined by a set of nodal points and their corresponding shape functions. These shape functions determine the interpolation of the element's unknowns within the element. The element stiffness matrix and load vector are then calculated using numerical integration techniques, and the element equations are assembled into the global system of equations for solution.