
Public Member Functions | |
| Lobatto (const unsigned int p=0) | |
Static Public Member Functions | |
| static std::vector< Polynomial < double > > | generate_complete_basis (const unsigned int p) |
Private Member Functions | |
| std::vector< double > | compute_coefficients (const unsigned int p) |
Lobatto polynomials of arbitrary degree on [0,1].
These polynomials are the integrated Legendre polynomials on [0,1]. The first two polynomials are the standard linear shape functions given by
and
. For
we use the definition
, where
denotes the
-th Legendre polynomial on
. The Lobatto polynomials
form a complete basis of the polynomials space of degree
.
Calling the constructor with a given index k will generate the polynomial with index k. But only for
the index equals the degree of the polynomial. For k==0 also a polynomial of degree 1 is generated.
These polynomials are used for the construction of the shape functions of Nédélec elements of arbitrary order.
Definition at line 540 of file polynomial.h.
| Polynomials::Lobatto::Lobatto | ( | const unsigned int | p = 0 | ) |
Constructor for polynomial of degree p. There is an exception for p==0, see the general documentation.
| static std::vector<Polynomial<double> > Polynomials::Lobatto::generate_complete_basis | ( | const unsigned int | p | ) | [static] |
Return the polynomials with index 0 up to degree. There is an exception for p==0, see the general documentation.
| std::vector<double> Polynomials::Lobatto::compute_coefficients | ( | const unsigned int | p | ) | [private] |
Compute coefficients recursively.
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