This module defines the UFL finite element classes.
This module provides an extensive list of predefined finite element families. Users or more likely, form compilers, may register new elements by calling the function register_element.
Register new finite element family
This module defines the UFL finite element classes.
Bases: ufl.finiteelement.finiteelementbase.FiniteElementBase
The vector sum of two finite element spaces:
EnrichedElement(V, Q) = {v + q | v in V, q in Q}.
Return whether the basis functions of this element is spatially constant over each cell.
Construct a new EnrichedElement object with some properties replaced with new values.
Format as string for pretty printing.
FEEC_aliases(name, cell, r, k):
name: “P Lambda” or “P- Lambda” cell: “interval”, “triangle”, “tetrahedron” r (polynomial degree): 1 <= r < ... k (form degree): 0 <= k <= n
where n is the topological dimension of the cell.
The families
P_r Lambda^k P-_r Lambda^k
map to H^1/H(curl)/H(div)/L^2 conforming finite element spaces based on the notation used in”Finite element exterior calculus, homological techniques and applications,”, Arnold, Falk and Winther, Acta Numerica, 2006, Table 5.1 and 5.2 (p. 60)
This module defines the UFL finite element classes.
Bases: ufl.finiteelement.finiteelementbase.FiniteElementBase
The basic finite element class for all simple finite elements
Create finite element
Construct a new FiniteElement object with some properties replaced with new values.
Format as string for pretty printing.
This module defines the UFL finite element classes.
Bases: object
Base class for all finite elements
Initialize basic finite element data
Return cell of finite element
Return the cell type onto which the element is restricted.
Return polynomial degree of finite element
Return the domain on which this element is defined.
Recursively extract component index relative to a (simple) element and that element for given value component index
Extract direct subelement index and subelement relative component index for a given component index
Return finite element family
Return whether the basis functions of this element is spatially constant over each cell.
Return number of sub elements
Return quadrature scheme of finite element
Return the regions referenced by this element and its subelements.
Return list of sub elements
Return the symmetry dict, which is a mapping c0 -> c1 meaning that component c0 is represented by component c1.
Return the shape of the value space
This module defines the UFL finite element classes.
Bases: ufl.finiteelement.finiteelementbase.FiniteElementBase
A finite element composed of a nested hierarchy of mixed or simple elements
Create mixed finite element from given list of elements
Return polynomial degree of finite element
Return the domain on which this element is defined.
Recursively extract component index relative to a (simple) element and that element for given value component index
Extract direct subelement index and subelement relative component index for a given component index
Return whether the basis functions of this element is spatially constant over each cell.
Return list of mixed sub elements.
Return number of mixed sub elements.
Return number of sub elements.
Construct a new MixedElement object with some properties replaced with new values.
Reconstruct a mixed element from new subelements.
Return the regions referenced by this element and its subelements.
Format as string for pretty printing.
Return list of sub elements.
Return the symmetry dict, which is a mapping c0 -> c1 meaning that component c0 is represented by component c1. A component is a tuple of one or more ints.
Bases: ufl.finiteelement.mixedelement.MixedElement
A special case of a mixed finite element where all elements are equal
Create tensor element (repeated mixed element with optional symmetries)
Extract direct subelement index and subelement relative component index for a given component index
Format as string for pretty printing.
Return the symmetry dict, which is a mapping c0 -> c1 meaning that component c0 is represented by component c1.
Bases: ufl.finiteelement.mixedelement.MixedElement
A special case of a mixed finite element where all elements are equal
Create vector element (repeated mixed element)
Format as string for pretty printing.
This module defines the UFL finite element classes.
Bases: ufl.finiteelement.finiteelementbase.FiniteElementBase
Represents the restriction of a finite element to a type of cell entity.
Return the domain onto which the element is restricted.
Return the element which is restricted.
Return whether the basis functions of this element is spatially constant over each cell.
Return number of restricted sub elements.
Return number of sub elements
Construct a new RestrictedElement object with some properties replaced with new values.
Return list of restricted sub elements.
Format as string for pretty printing.
Return list of sub elements
Return the symmetry dict, which is a mapping c0 -> c1 meaning that component c0 is represented by component c1.
This module defines the UFL finite element classes.
Bases: ufl.finiteelement.finiteelementbase.FiniteElementBase
The tensor product of d element spaces:
Given bases {phi_i} for V_i for i = 1, ...., d, { phi_0 * phi_1 * ... * phi_d } forms a basis for V.
Create TensorProductElement from a given list of elements.
Return number of subelements.
Return number of tensorproduct sub elements.
Short pretty-print.
Return subelements (factors).
Return list of tensorproduct sub elements.