template<typename FieldType, int k, int d, Dune::GeometryType::BasicType bt, typename ComputationFieldType = FieldType, BasisType basisType = BasisType::Pk>
class Dune::PB::OrthonormalPolynomialBasis< FieldType, k, d, bt, ComputationFieldType, basisType >
Integrate monomials over the reference element.
Computes an L_2 orthonormal basis of P_k on the given reference element. The basis polynomials are stored in a monomial representation. With the matrix coeffs private to this class we have
with n_k : the dimension of P_k alpha_j : the exponents of the j-th monomial
The class can be used to evaluate polynomials with any degree l smaller or equal to the compile-time parameter k.
Calculating derivatives. From (1) we have
where beta_jr = alpha_jr-1 if r=s and alpha_jr else.
Template Parameters
FieldType
Type to represent coefficients after computation.
k
The polynomial degreee.
d
The space dimension.
GeometryType::BasicType
The reference element
ComputationFieldType
Type to do computations with. Might be high precission.