Problem Description

Solution

How elements are defined and used in COMSOL Multiphysics

The use of elements in defining a finite element model in COMSOL Multiphysics differs significantly from the procedure in traditional FEA software. In COMSOL Multiphysics, a finite element consists of an element shape function, typically a multivariate piece-wise polynomial, together with a mesh element of a certain geometric shape (tetrahedral, hexahedral, etc.)

This framework allows COMSOL Multiphysics to generate the necessary multiphysics (or single physics) elements on-the-fly based on the equations and couplings the user has provided. For example, a 3D tetrahedral thermal stress element would automatically be generated when defining a 3D heat transfer equation coupled with structural analysis and specifying an unstructured mesh.

This flexibility on the element level makes it possible to easily create unlimited multiphysics couplings, since the possibilities are not narrowed down by a given collection of predefined elements. Neither is there a need to program models on an element level, because the necessary elements are automatically generated based on the equations, mesh elements, and the respective shape functions for the variables in the model.

Finite Element Types Supported in COMSOL Multiphysics

Using traditional FEA terminology, you can say that COMSOL Multiphysics comes with isoparametric elements of order 1 to 5 in 2D and order 1 to 4 in 3D. Isoparametric elements are called Lagrange elements in COMSOL Multiphysics. (This should not be confused with Lagrange polynomials, which is something else.) The geometric shapes of the elements can be triangular and quadrilateral in 2D and tetrahedral, hexahedral, and prismatic (with triangular base) in 3D. The Lagrange elements support arbitrary multiphysics combinations. For certain types of physics other element types (or rather shape functions) are more efficient and such specialized element types are available in the add-on modules (see below).

Additional Element Types Available in COMSOL Multiphysics and the Add-on Modules

• The Chemical Engineering, MEMS, and Heat Transfer Modules additionally support special elements for fluid flow as modeled with the Navier-Stokes equations. The supported element types consist of combinations of Lagrange elements, so called bubble elements, and discontinuous elements.
• The AC/DC Module and the RF Module additionally support vector elements in applications where it is needed for discretizing equations that include the differential operator commonly called rot or curl. These elements are also called edge elements. Vector elements of order 1 to 3 are available in 2D and 3D.
• The Structural Mechanics Module additionally supports shell elements, plate elements, beam elements, and bar elements. There is also a plasticity element for accelerated solution of problems with nonlinear plastic material models (also included in the MEMS module).
• The Heat Transfer Module has a specialized radiation element for surface-to-surface heat radiation problems.

In addition to the above element types, COMSOL Multiphysics also supports so called Hermite elements of order 3 to 5 in 2D and order 3 to 4 in 3D and also so called Argyris elements of order 5 in 2D.

Element order versus geometry shape order

For higher-order elements, COMSOL Multiphysics allows you to choose the geometry shape order. The latter is defined as the order of polynomial functions used to approximate the geometric boundaries and edges. This setting is available in Model Settings, under the Physics menu. By default, geometry shape order is set to Automatic, and COMSOL computes this order from the shape functions in the model. The geometry order will then equal the highest order of shape functions in each geometry. You can set explicit geometry order to override this behavior. Setting geometry shape order to Linear often helps avoid inverted elements, without sacrificing the accuracy provided by higher-order elements. If first-order derivatives must be computed from the solution variables, it is often imperative to keep the order of elements high and set geometry shape order to Linear. On the other hand, setting geometry shape to a higher order than the element order is not meaningful.

For further information about each of the element types, see "Understanding the Finite Element Method" in the COMSOL Multiphysics Reference Guide.

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