Dune::Fem::HdivProjection< DiscreteFunctionType > Class Template Reference

H-div Projection for discontinuous discrete functions. The projection is described in detail in: More...

#include <dune/fem/operator/projection/hdivprojection.hh>

Public Types
typedef DiscreteFunctionType	DestinationType
	type of argument and destination
typedef DiscreteFunctionSpaceType	SpaceType
	convenience typedef for space type

Public Member Functions
	HdivProjection (const DiscreteFunctionSpaceType &space)
	constructor taking space
const DiscreteFunctionSpaceType &	space () const
	return reference to space
void	setTime (double)
	set time for operators More...
double	timeStepEstimate () const
	estimate maximum time step More...
virtual void	operator() (const DiscreteFunctionType &arg, DiscreteFunctionType &dest) const
	application operator projection arg to H-div space
virtual int	size () const
	return size of discrete function space, i.e. number of unknowns
virtual void	initializeTimeStepSize (const DestinationType &U0) const
	call operator once to calculate initial time step size More...
virtual bool	hasLimiter () const
	return true if limit method is implemented More...
virtual void	limit (const DestinationType &arg, DestinationType &dest) const
	limiter application operator More...
virtual void	applyLimiter (DestinationType &U) const
	limiter application operator More...
virtual const DestinationType *	destination () const
	return reference to pass's local memory
virtual void	jacobian (const DomainFunctionType &u, JacobianOperatorType &jOp) const=0
	obtain linearization More...
virtual void	operator() (const DomainFunctionType &u, RangeFunctionType &w) const=0
	application operator More...
virtual void	finalize ()
	finalization of operator More...

Static Public Member Functions
static double	normalJump (const DiscreteFunctionType &discFunc, const int polyOrder=-1)
	return sum of jumps of discrete function normal to intersection

Detailed Description

template<class DiscreteFunctionType>
class Dune::Fem::HdivProjection< DiscreteFunctionType >

H-div Projection for discontinuous discrete functions. The projection is described in detail in:

P. Bastian and B. Riviere. Superconvergence and H(div)-projection for discontinuous Galerkin methods. Int. J. Numer. Meth. Fluids., 42:1043-1057, 2003.

(see homepage of Peter Bastian: http://hal.iwr.uni-heidelberg.de/~peter/Papers/BDMpaper.pdf )

Note:

This projection only works for polynomial order 1 and the following spaces:

• SimplexGrids + DiscontinuousGalerkinSpace
• CubeGrids + LegendreDiscontinuousGalerkinSpace

Member Function Documentation

applyLimiter()

virtual void Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType , Fem::AutomaticDifferenceOperator< DiscreteFunctionType > >::applyLimiter ( DestinationType &  U ) const

inlinevirtualinherited

limiter application operator

Parameters

[in,out]

U

argument and destination to apply Limiter(u), needs internal copying

Note

: Default implementation is to do nothing (hasLimiter == false)

finalize()

virtual void Dune::Fem::Operator< JacobianOperator::DomainFunctionType , JacobianOperator::RangeFunctionType >::finalize ( )

inlinevirtualinherited

finalization of operator

Note

The default implementation is empty.

hasLimiter()

virtual bool Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType , Fem::AutomaticDifferenceOperator< DiscreteFunctionType > >::hasLimiter ( ) const

inlinevirtualinherited

return true if limit method is implemented

Returns

true if limit is implemented

initializeTimeStepSize()

void Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType , Fem::AutomaticDifferenceOperator< DiscreteFunctionType > >::initializeTimeStepSize ( const DestinationType &  U0 ) const

inlinevirtualinherited

call operator once to calculate initial time step size

Parameters

U0	initial data to compute initial time step size

jacobian()

virtual void Dune::Fem::DifferentiableOperator< AutomaticDifferenceLinearOperator< DomainFunction, DomainFunction > >::jacobian ( const DomainFunctionType &  u, JacobianOperatorType &  jOp  ) const

pure virtualinherited

obtain linearization

Parameters

[in]	u	argument discrete function
[out]	jOp	destination Jacobian operator

Note

This method has to be implemented by all derived classes.

limit()

virtual void Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType , Fem::AutomaticDifferenceOperator< DiscreteFunctionType > >::limit ( const DestinationType &  arg, DestinationType &  dest  ) const

inlinevirtualinherited

limiter application operator

Parameters

arg	argument, u
dest	destination, Limiter(u)

Note

: Default implementation is to copy arg into dest.

operator()()

virtual void Dune::Fem::Operator< JacobianOperator::DomainFunctionType , JacobianOperator::RangeFunctionType >::operator() ( const DomainFunctionType &  u, RangeFunctionType &  w  ) const

pure virtualinherited

application operator

Parameters

[in]	u	argument discrete function
[out]	w	destination discrete function

Note

This method has to be implemented by all derived classes.

Implemented in EllipticOperator< JacobianOperator::DomainFunctionType, JacobianOperator::RangeFunctionType, Model >.

setTime()

template<class DiscreteFunctionType >

void Dune::Fem::HdivProjection< DiscreteFunctionType >::setTime ( double  time )

inlinevirtual

set time for operators

Parameters

time	current time of evaluation

Reimplemented from Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType >.

timeStepEstimate()

template<class DiscreteFunctionType >

double Dune::Fem::HdivProjection< DiscreteFunctionType >::timeStepEstimate ( ) const

inlinevirtual

estimate maximum time step

For an explicit time discretization, the time step has to be limited. An estimate for the maximum time step of an explicit Euler scheme is returned by this function. Maximum time steps for higher order Runge Kutta schemes can be derived from this value.

Reimplemented from Dune::Fem::SpaceOperatorInterface< DiscreteFunctionType >.

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

• dune/fem/operator/projection/hdivprojection.hh