};
-/**
- * 8-Point-Gauss quadrature formula, exact for polynomials of degree 15.
- * I have not found explicite
- * representations of the zeros of the Legendre functions of sixth
- * and higher degree. If anyone finds them, please replace the existing
- * numbers by these expressions.
- *
- * Reference: J. E. Akin: "Application and Implementation of Finite
- * Element Methods"
- * For a comprehensive list of Gaussian quadrature formulae, see also:
- * A. H. Strout, D. Secrest: "Gaussian Quadrature Formulas"
- */
-template <int dim>
-class QGauss8 : public Quadrature<dim>
-{
- public:
- QGauss8 ();
-};
-
-
/**
* Midpoint quadrature rule, exact for linear polynomials.
*/
};
-template <>
-QGauss8<1>::QGauss8 () :
- Quadrature<1> (8)
-{
- // points on [-1,1]
- static const double xpts_normal[] = { -0.960289856497536,
- -0.796666477413627,
- -0.525532409916329,
- -0.183434642495650,
- +0.183434642495650,
- +0.525532409916329,
- +0.796666477413627,
- +0.960289856497536 };
- // weights on [-1,1]
- static const double wts_normal[] = { 0.101228536200376,
- 0.222381034453374,
- 0.313706645877887,
- 0.362683783378362,
- 0.362683783378362,
- 0.313706645877887,
- 0.222381034453374,
- 0.101228536200376 };
-
- // points and weights on [0,1]
- static const double xpts[] = { (xpts_normal[0]+1)/2.,
- (xpts_normal[1]+1)/2.,
- (xpts_normal[2]+1)/2.,
- (xpts_normal[3]+1)/2.,
- (xpts_normal[4]+1)/2.,
- (xpts_normal[5]+1)/2.,
- (xpts_normal[6]+1)/2.,
- (xpts_normal[7]+1)/2. };
- static const double wts[] = { wts_normal[0]/2.,
- wts_normal[1]/2.,
- wts_normal[2]/2.,
- wts_normal[3]/2.,
- wts_normal[4]/2.,
- wts_normal[5]/2.,
- wts_normal[6]/2.,
- wts_normal[7]/2. };
-
- for (unsigned int i=0; i<n_quadrature_points; ++i)
- {
- quadrature_points[i] = Point<1>(xpts[i]);
- weights[i] = wts[i];
- };
-};
-
template <>
QMidpoint<1>::QMidpoint () :
QGauss7<dim>::QGauss7 () :
Quadrature<dim> (QGauss7<dim-1>(), QGauss7<1>()){};
-template <int dim>
-QGauss8<dim>::QGauss8 () :
- Quadrature<dim> (QGauss8<dim-1>(), QGauss8<1>()){};
-
template <int dim>
QMidpoint<dim>::QMidpoint () :
template class QGauss5<2>;
template class QGauss6<2>;
template class QGauss7<2>;
-template class QGauss8<2>;
template class QMidpoint<2>;
template class QTrapez<2>;
template class QSimpson<2>;
template class QGauss5<3>;
template class QGauss6<3>;
template class QGauss7<3>;
-template class QGauss8<3>;
template class QMidpoint<3>;
template class QTrapez<3>;
template class QSimpson<3>;