Normal stabilization for elasticity in DG FEM in 2D. More...

#include <bilinearForm.hh>

Inheritance diagram for DGElasticNormalStabBf2d:

Collaboration diagram for DGElasticNormalStabBf2d:

Public Member Functions
virtual DGElasticNormalStabBf2d *	clone () const
	Virtual constructor.
	DGElasticNormalStabBf2d (const Real omega, const uint dV, const uint dU, concepts::BoundaryConditions *bc)
	Constructor.
virtual void	operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em)=0
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`.
virtual void	operator() (const concepts::Element< Real > &elmV, const concepts::Element< Real > &elmU, concepts::ElementMatrix< Real > &em)
	Application operator for volume terms, does nothing.
virtual void	operator() (const concepts::Element< Real > &elmV, const concepts::Element< Real > &elmU, concepts::ElementMatrix< Real > &em, const concepts::ElementPair< Real > &ep)
	Application operator for DG term.
virtual void	operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em, const ElementPair< typename Realtype< Real >::type > &ep)
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
concepts::BoundaryConditions *	bc_
	Boundary conditions, only the boundary type is relevant.
const uint	dU_
	Number of vectorial dimension of ansatz function.
const uint	dV_
	Number of vectorial dimension of test function.
const Real	omega_
	Stabilizing parameter.

Detailed Description

Normal stabilization for elasticity in DG FEM in 2D.

This bilinear form integrates

$\frac{\omega}{h} \int_{e} [\phi_i^{\top} \cdot n_e] [\phi_j \cdot n_e] \, ds.$

where h is an appropriate measure for local mesh size

Author:: Christoph Winkelmann, 2003

Definition at line 118 of file bilinearForm.hh.

Constructor & Destructor Documentation

DGElasticNormalStabBf2d::DGElasticNormalStabBf2d	(	const Real	omega,
		const uint	dV,
		const uint	dU,
		concepts::BoundaryConditions *	bc
	)		`[inline]`

Constructor.

Parameters:

omega	Stabilizing parameter
dV	Number of vectorial dimension of test function
dU	Number of vectorial dimension of ansatz function
bc	Boundary conditions, only the boundary type is relevant

Definition at line 126 of file bilinearForm.hh.

Member Function Documentation

virtual DGElasticNormalStabBf2d* DGElasticNormalStabBf2d::clone ( ) const [inline, virtual]

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

Implements concepts::Cloneable.

Definition at line 140 of file bilinearForm.hh.

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virtual std::ostream& concepts::BilinearForm< Real , typename Realtype<Real >::type >::info ( std::ostream & os ) const [protected, virtual, inherited]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Reimplemented in hp2D::DiffussionReaction, TraceMass, hp2D::DivDiv< Weight >, hp2D::RotRot, hp2Dedge::RotRot, hp2Dedge::Identity, hp2Dedge::Graduv, hp2Dedge::EdgeIdentity, hp3D::Laplace, hp3D::Identity, hp3D::DivDiv< Weight >, hp3D::Hook, and hp3D::RotRot.

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator()	(	const Element< typename Realtype<Real >::type > &	elmX,
		const Element< typename Realtype<Real >::type > &	elmY,
		ElementMatrix< Real > &	em,
		const ElementPair< typename Realtype<Real >::type > &	ep
	)		`[inline, virtual, inherited]`

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

If this method is not reimplemented in a derived class, the default behaviour is to call the application operator without ep.

Postcondition:: The returned matrix em has the correct size.

Parameters:

elmX	Left element
elmY	Right element
em	Return element matrix
ep	Element pair holding more information on the pair `elmX` and `elmY`

Definition at line 53 of file bilinearForm.hh.

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virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator()	(	const Element< typename Realtype<Real >::type > &	elmX,
		const Element< typename Realtype<Real >::type > &	elmY,
		ElementMatrix< Real > &	em
	)		`[pure virtual, inherited]`

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

Postcondition:: The returned matrix em has the correct size.

Parameters:

elmX	Left element (test functions)
elmY	Right element (trial functions)
em	Return element matrix

virtual void DGElasticNormalStabBf2d::operator()	(	const concepts::Element< Real > &	elmV,
		const concepts::Element< Real > &	elmU,
		concepts::ElementMatrix< Real > &	em
	)		`[inline, virtual]`

Application operator for volume terms, does nothing.

Definition at line 130 of file bilinearForm.hh.

virtual void DGElasticNormalStabBf2d::operator()	(	const concepts::Element< Real > &	elmV,
		const concepts::Element< Real > &	elmU,
		concepts::ElementMatrix< Real > &	em,
		const concepts::ElementPair< Real > &	ep
	)		`[virtual]`