symfem.polynomials.lobatto

Lobatto polynomials.

Module Contents

Functions

lobatto_basis_interval(...)	Get Lobatto polynomials on an interval.
lobatto_dual_basis_interval(...)	Get L2 dual of Lobatto polynomials on an interval.
lobatto_basis(→ List[symfem.functions.ScalarFunction])	Get Lobatto polynomials.
lobatto_dual_basis(→ List[symfem.functions.ScalarFunction])	Get L2 dual of Lobatto polynomials.

symfem.polynomials.lobatto.lobatto_basis_interval(order: int) → List[symfem.functions.ScalarFunction]

Get Lobatto polynomials on an interval.

Parameters:

order – The maximum polynomial degree

Returns:

Lobatto polynomials

symfem.polynomials.lobatto.lobatto_dual_basis_interval(order: int) → List[symfem.functions.ScalarFunction]

Get L2 dual of Lobatto polynomials on an interval.

Parameters:

order – The maximum polynomial degree

Returns:

Dual Lobatto polynomials

symfem.polynomials.lobatto.lobatto_basis(cell: str, order: int, include_endpoints: bool = True) → List[symfem.functions.ScalarFunction]

Get Lobatto polynomials.

Parameters:

• cell – The cell type

• order – The maximum polynomial degree

• include_endpoint – should polynomials that are non-zero on the boundary be included?

Returns:

Lobatto polynomials

symfem.polynomials.lobatto.lobatto_dual_basis(cell: str, order: int, include_endpoints: bool = True) → List[symfem.functions.ScalarFunction]

Get L2 dual of Lobatto polynomials.

Parameters:

• cell – The cell type

• order – The maximum polynomial degree

• include_endpoint – should polynomials that are non-zero on the boundary be included?

Returns:

Lobatto polynomials