puncturedfem.LocalPolynomial

Polynomial on a mesh cell.

A typical use case for this class is to represent a polynomial part of a local Poisson function.

The weighted normal derivative of the polynomial and that of its anti-Laplacian are computed and stored in their respective DirichletTrace objects.

Attributes:

Name	Type	Description
exact_form	Polynomial	Exact form of the polynomial.
trace	DirichletTrace	Dirichlet trace of the polynomial.
grad1	Polynomial	First gradient of the polynomial.
grad2	Polynomial	Second gradient of the polynomial.
antilap	Polynomial	Anti-Laplacian of the polynomial.
antilap_trace	DirichletTrace	Dirichlet trace of the anti-Laplacian.

__add__(other)

Add two local polynomials.

Parameters:

Name	Type	Description	Default
other	LocalPolynomial	The other local polynomial.	required

Returns:

Type	Description
LocalPolynomial	The sum of the two local polynomials.

__init__(exact_form, mesh_cell)

Initialize the polynomial.

Parameters:

Name	Type	Description	Default
exact_form	Polynomial	Exact form of the polynomial.	required
mesh_cell	MeshCell	The mesh cell on which the polynomial is defined.	required

__mul__(other)

Multiply a local polynomial by a scalar.

Parameters:

Name	Type	Description	Default
other	Union[int, float]	The scalar.	required

Returns:

Type	Description
LocalPolynomial	The product of the local polynomial and the scalar.

__rmul__(other)

Multiply a local polynomial by a scalar.

Parameters:

Name	Type	Description	Default
other	Union[int, float]	The scalar.	required

Returns:

Type	Description
LocalPolynomial	The product of the local polynomial and the scalar.

__sub__(other)

Subtract two local polynomials.

Parameters:

Name	Type	Description	Default
other	LocalPolynomial	The other local polynomial.	required

Returns:

Type	Description
LocalPolynomial	The difference of the two local polynomials.

__truediv__(other)

Divide a local polynomial by a scalar.

Parameters:

Name	Type	Description	Default
other	Union[int, float]	The scalar.	required

Returns:

Type	Description
LocalPolynomial	The division of the local polynomial by the scalar.