StokesIntegrators::PolynomialError< dim > Class Template Reference

#include <polynomial.h>

Inheritance diagram for StokesIntegrators::PolynomialError< dim >:

Collaboration diagram for StokesIntegrators::PolynomialError< dim >:

Public Member Functions
	PolynomialError (const Polynomials::Polynomial< double > curl_potential_1d, const Polynomials::Polynomial< double > grad_potential_1d)
virtual void	cell (DoFInfo< dim > &dinfo, IntegrationInfo< dim > &info) const
virtual void	boundary (DoFInfo< dim > &dinfo, IntegrationInfo< dim > &info) const
virtual void	face (DoFInfo< dim > &dinfo1, DoFInfo< dim > &dinfo2, IntegrationInfo< dim > &info1, IntegrationInfo< dim > &info2) const
Public Member Functions inherited from AmandusIntegrator< dim >
	AmandusIntegrator ()
virtual void	extract_data (const dealii::AnyData &data)
	Extract data independent of the cell. More...
unsigned int	n_errors () const
unsigned int	error_type (unsigned int i) const
std::string	error_name (unsigned int i) const
dealii::UpdateFlags	update_flags () const
	Returns the update flags to be used. More...
dealii::UpdateFlags	update_flags_face () const
	Returns the update flags to be used on boundary and interior faces. More...
void	add_flags (const dealii::UpdateFlags flags)
	Add update flags on all objects. More...
void	add_flags_face (const dealii::UpdateFlags flags)
	Add update flags on boundary and internal faces. More...

Private Attributes
Polynomials::Polynomial< double >	curl_potential_1d
Polynomials::Polynomial< double >	grad_potential_1d

Additional Inherited Members
Public Attributes inherited from AmandusIntegrator< dim >
double	timestep
	Current timestep if applicable. More...
dealii::SmartPointer< dealii::Quadrature< dim > >	cell_quadrature
	Quadrature rule used on cells. More...
dealii::SmartPointer< dealii::Quadrature< dim-1 > >	boundary_quadrature
	Quadrature rule used on boundary faces. More...
dealii::SmartPointer< dealii::Quadrature< dim-1 > >	face_quadrature
	Quadrature rule used on faces. More...
Protected Attributes inherited from AmandusIntegrator< dim >
std::vector< unsigned int >	error_types
std::vector< std::string >	error_names

Detailed Description

template<int dim>
class StokesIntegrators::PolynomialError< dim >

Computes the error between a numerical solution and a known exact polynomial solution of a Stokes problem.

For two dimensions, the two constructor arguments are two one-dimensional polynomials \(\psi(t)\) and \(\phi(t)\). The solution to such the Stokes problem is then determined as

\begin{alignat*}{2} \mathbf u &= \nabla\times \Psi \qquad\qquad & \Psi((x_1,\ldots,x_d) &= \prod \psi(x_i) \\ p &= \Phi & \Phi((x_1,\ldots,x_d) &= \prod \phi(x_i) \end{alignat*}

The according right hand sides of the Stokes equations and the residuals are integrated by the functions of the classes PolynomialRHS and PolynomialResidual.

If computing on a square, say \([-1,1]^2\), the boundary conditions of the Stokes problem are determined as follows: if \(\psi(-1)=\psi(1)=0\), the velocity has the boundary condition \(\mathbf u\cdot \mathbf n=0\) (slip). If in addition \(\psi'(-1)=\psi'(1)=0\), then there holds on the boundary \(\mathbf u=0\) (no-slip).

Note

No reasonable iplementation for three dimensions is provided.

Author

Guido Kanschat

Date

2014

Constructor & Destructor Documentation

template<int dim>

StokesIntegrators::PolynomialError< dim >::PolynomialError	(	const Polynomials::Polynomial< double >	curl_potential_1d,
		const Polynomials::Polynomial< double >	grad_potential_1d
	)

Member Function Documentation

template<int dim>

void StokesIntegrators::PolynomialError< dim >::boundary ( DoFInfo< dim > &  dinfo, IntegrationInfo< dim > &  info  ) const

virtual

template<int dim>

void StokesIntegrators::PolynomialError< dim >::cell ( DoFInfo< dim > &  dinfo, IntegrationInfo< dim > &  info  ) const

virtual

Here is the call graph for this function:

template<int dim>

void StokesIntegrators::PolynomialError< dim >::face ( DoFInfo< dim > &  dinfo1, DoFInfo< dim > &  dinfo2, IntegrationInfo< dim > &  info1, IntegrationInfo< dim > &  info2  ) const

virtual

Member Data Documentation

template<int dim>

Polynomials::Polynomial<double> StokesIntegrators::PolynomialError< dim >::curl_potential_1d

private

template<int dim>

Polynomials::Polynomial<double> StokesIntegrators::PolynomialError< dim >::grad_potential_1d

private

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The documentation for this class was generated from the following file:

• stokes/polynomial.h