Rodin::Variational::P0Element class

Degree 0 Lagrange element.

Template parameters
Scalar	Type of scalar range (e.g., Real, Complex)

Piecewise constant (degree 0) scalar Lagrange element.

Specialization	Description
P0Element<Scalar>	Scalar-valued discontinuous piecewise constant element.
P0Element<SpatialVector<Scalar>>	Vector-valued discontinuous piecewise constant element.

The P0Element represents a piecewise constant finite element with:

DOF count: 1 per element (located at barycenter)
Basis function: for all in element
Derivatives: (constant function has zero gradient)

P0 elements are discontinuous across element interfaces, making them suitable for DG methods, flux computations, and element-wise constant approximations.

Base classes

template<class Derived> class FiniteElementBase<P0Element<Scalar>>: Base class for finite elements.

Public types

class BasisFunction: Represents the constant basis function of a P0 scalar element.
class LinearForm: Represents a linear form of a P0 scalar element.
using Parent = FiniteElementBase<P0Element<Scalar>>: Parent class.
using ScalarType = Scalar: Scalar value type.
using RangeType = Scalar: Type of range.

Constructors, destructors, conversion operators

P0Element(Geometry::Polytope::Type geometry) constexpr: Constructs the P0Element from the given arguments.
P0Element(const P0Element& other) constexpr: Copy constructor.
P0Element(P0Element&& other) constexpr: Move constructor.

Public functions

auto getCount() const -> size_t constexpr: Gets the number of degrees of freedom in the finite element.
auto getNode(size_t i) const -> const Math::SpatialVector<Real>&: Gets the node of a local degree of freedom.
auto getLinearForm(size_t) const -> LinearForm constexpr: Gets the degree-of-freedom functional of a local degree of freedom.
auto getBasis(size_t) const -> BasisFunction constexpr: Gets the basis function of a local degree of freedom.
auto getOrder() const -> size_t constexpr: Returns the polynomial order.

Function documentation

template<class Scalar>
size_t Rodin::Variational::P0Element<Scalar>::getCount() const constexpr

Gets the number of degrees of freedom in the finite element.

Returns	Number of degrees of freedom