Rectangular higher order edge element (finite element method)

In summary, a rectangular higher order edge element is a type of finite element used in numerical analysis to solve partial differential equations. It is defined by four corner nodes and uses higher degree polynomials to improve solution accuracy. Compared to other finite element types, it has a higher order of continuity and polynomial order, making it better at approximating solutions with complex boundary conditions. However, it also has a higher computational cost and can be challenging to implement. Some advantages of using rectangular higher order edge elements include their accuracy in capturing complex solutions and higher convergence rate. Future improvements include more efficient numerical algorithms, advancements in computing technology, and ongoing research in the field.
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mdn
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I have solved many finite element problems using nodal based (rectangular element) for higher order. now i am trying to solve electromagnetic problem using vector element (Nedelec or Whitney). I know only triangular edge based element with first order only and not higher order. i am searching this higher order **rectangular** edge based element but unable to find it. is there any higher order rectangular edge element?
 
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Yes, there are higher order rectangular edge elements that can be used in finite element method for solving electromagnetic problems. One such element is the Serendipity element, which is a higher order rectangular element with edges that can be used for vector fields. This element has nodal points at the midpoints of the edges, allowing for higher order interpolation and accurate representation of the vector field. Other higher order rectangular edge elements such as the Lagrange element and the Hermite element can also be used for solving electromagnetic problems. These elements have additional degrees of freedom compared to the first order triangular edge elements, allowing for a more accurate solution. It is important to carefully select the appropriate element for the specific problem being solved in order to achieve accurate results.
 

FAQ: Rectangular higher order edge element (finite element method)

What is a rectangular higher order edge element?

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.

How does a rectangular higher order edge element differ from a standard rectangular element?

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.

What are the advantages of using a rectangular higher order edge element?

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.

What are some applications of the rectangular higher order edge element?

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.

How is a rectangular higher order edge element implemented in the finite element method?

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.

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