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AbstractMeshField_ is defined to contain the element level data inside a finite element. In simple terms it contains Scalar, Vector, and Tensor data defined inside the element of finite element mesh.


ScalarMeshField is a subclass of AbstractMeshField. It is used to store scalar variables defined on elements of mesh. We can define the variable either on the nodes of the finite element, or we can define these variables on the quadrature points.


STScalarMeshField is a subclass of AbstractMeshField. You can see its structure here


STVectorMeshField is an instance of AbstractMeshField. It is designed to keep the space-time values of vector field inside an element.


VectorMeshField is a subclass of AbstractMeshField_. It is designed for storing the vector data which is defined on elements of mesh. The vector field can be defined on the nodes of element or on the quadrature point of elements.