Lagrange shape functions of first order. More...

#include <lagrangep1.h>

Inheritance diagram for ug::LagrangeP1< TRefElem >:

Public Types
typedef base_type::grad_type	grad_type
	Gradient type.

typedef TRefElem	reference_element_type
	Reference Element type.

typedef base_type::shape_type	shape_type
	Shape type.

Public Types inherited from ug::BaseLSFS< LagrangeP1< TRefElem >, TRefElem::dim >
typedef MathVector< TDim >	grad_type
	Gradient type.

typedef LagrangeP1< TRefElem >	ImplType
	type of implementation

typedef number	shape_type
	Shape type.

Public Member Functions
bool	continuous () const
	returns if space constructs continuous functions

void	grad (grad_type &value, size_t i, const MathVector< dim > &x) const
	evaluates the gradient of the shape function

	LagrangeP1 ()
	constructor

size_t	num_sh () const

bool	position (size_t i, MathVector< dim > &pos) const
	local position of DoF i

shape_type	shape (size_t i, const MathVector< dim > &x) const
	evaluates the shape function

Public Member Functions inherited from ug::LagrangeLDS< TRefElem >
bool	exact_position_available () const
	returns if the local dof position are exact

	LagrangeLDS (size_t order=1)
	constructor

const LocalDoF &	local_dof (size_t dof) const
	returns the dof storage

size_t	num_dof () const
	returns the total number of DoFs on the finite element

size_t	num_dof (ReferenceObjectID roid) const
	returns the number of DoFs on a sub-geometric object type

ReferenceObjectID	roid () const
	returns the type of reference element

void	set_order (size_t order)
	sets the order

Public Member Functions inherited from ug::LocalDoFSet
int	dim () const
	returns the reference dimension

size_t	num_dof (int d, size_t id) const
	returns the number of DoFs on a sub-geometric object of dim and id

bool	operator!= (const LocalDoFSet &v) const
	inequality check

bool	operator== (const LocalDoFSet &v) const
	equality check

virtual	~LocalDoFSet ()
	virtual destructor

size_t	num_dof () const

Public Member Functions inherited from ug::BaseLSFS< LagrangeP1< TRefElem >, TRefElem::dim >
void	grad (grad_type &g, size_t i, const MathVector< dim > &x) const
	evaluates the gradient of the shape function

void	grads (grad_type *vGrad, const MathVector< dim > &x) const
	returns all gradients evaluated at a point

void	grads (std::vector< grad_type > &vGrad, const MathVector< dim > &x) const
	returns all gradients evaluated at a point

void	grads (std::vector< std::vector< grad_type > > &vvGrad, const std::vector< MathVector< dim > > &vLocPos) const
	returns all gradients evaluated at a point

void	shape (shape_type &sh, size_t i, const MathVector< dim > &x) const
	evaluates the shape function

shape_type	shape (size_t i, const MathVector< dim > &x) const
	evaluates the shape function

void	shapes (shape_type *vShape, const MathVector< dim > &x) const
	returns all shape functions evaluated at a point

void	shapes (std::vector< shape_type > &vShape, const MathVector< dim > &x) const
	returns all shape functions evaluated at a point

void	shapes (std::vector< std::vector< shape_type > > &vvShape, const std::vector< MathVector< dim > > &vLocPos) const
	returns all shape functions evaluated at a point

Static Public Attributes
static const int	dim = TRefElem::dim
	Dimension, where shape functions are defined.

static const size_t	nsh = TRefElem::numCorners
	Number of shape functions.

static const size_t	order = 1
	Order of Shape functions.

Static Public Attributes inherited from ug::BaseLSFS< LagrangeP1< TRefElem >, TRefElem::dim >
static const int	dim
	dimension of reference element

Private Types
typedef BaseLSFS< LagrangeP1< TRefElem >, TRefElem::dim >	base_type
	base class

Additional Inherited Members
Protected Member Functions inherited from ug::BaseLSFS< LagrangeP1< TRefElem >, TRefElem::dim >
ImplType &	getImpl ()
	access to implementation

const ImplType &	getImpl () const
	const access to implementation

Protected Attributes inherited from ug::LagrangeLDS< TRefElem >
std::vector< LocalDoF >	m_vLocalDoF
	association to geom obj

size_t	p
	order

Detailed Description

template<typename TRefElem>
class ug::LagrangeP1< TRefElem >

Lagrange shape functions of first order.

This class provides Lagrangian Shape Functions of order 1 for a Reference Element.

Template Parameters

TRefElem Reference Element Type

Member Typedef Documentation

◆ base_type

template<typename TRefElem >

typedef BaseLSFS<LagrangeP1<TRefElem>, TRefElem::dim> ug::LagrangeP1< TRefElem >::base_type

private

base class

◆ grad_type

template<typename TRefElem >

typedef base_type::grad_type ug::LagrangeP1< TRefElem >::grad_type

Gradient type.

◆ reference_element_type

template<typename TRefElem >

typedef TRefElem ug::LagrangeP1< TRefElem >::reference_element_type

Reference Element type.

◆ shape_type

template<typename TRefElem >

typedef base_type::shape_type ug::LagrangeP1< TRefElem >::shape_type

Shape type.

Constructor & Destructor Documentation

◆ LagrangeP1()

template<typename TRefElem >

ug::LagrangeP1< TRefElem >::LagrangeP1 ( )

inline

constructor

Member Function Documentation

◆ continuous()

template<typename TRefElem >

bool ug::LagrangeP1< TRefElem >::continuous ( ) const

inline

returns if space constructs continuous functions

◆ grad()

template<typename TRefElem >

void ug::LagrangeP1< TRefElem >::grad	(	grad_type &	value,
		size_t	i,
		const MathVector< dim > &	x
	)		const

evaluates the gradient of the shape function

This function returns the gradient of Shape Function i at an element-local evaluation point.

Parameters

[in]	i	number of DoF
[in]	x	Position on reference element (evaluation point)

Returns: gradient at point

◆ num_sh()

template<typename TRefElem >

size_t ug::LagrangeP1< TRefElem >::num_sh ( ) const

inlinevirtual

returns the total number of dofs on the finite element

Reimplemented from ug::LocalDoFSet.

References ug::LagrangeP1< TRefElem >::nsh.

Referenced by ug::FV1InnerBoundaryElemDisc< TImpl, TDomain >::prep_err_est_elem(), and ug::FV1InnerBoundaryElemDisc< TImpl, TDomain >::prep_err_est_elem_loop().

◆ position()

template<typename TRefElem >

bool ug::LagrangeP1< TRefElem >::position	(	size_t	i,
		MathVector< dim > &	pos
	)		const

local position of DoF i

This function returns the local position of a DoF if possible.

Parameters

[in]	i	number of DoF
[out]	pos	Position of DoF

Return values

true	if position exists
false	if no meaningful position available

◆ shape()

template<typename TRefElem >

shape_type ug::LagrangeP1< TRefElem >::shape	(	size_t	i,
		const MathVector< dim > &	x
	)		const

evaluates the shape function

This function returns the value of Shape Function i at an element-local evaluation point.

Parameters

[in]	i	number of DoF
[in]	x	Position on reference element (evaluation point)

Returns: shape function value at point

Member Data Documentation

◆ dim

template<typename TRefElem >

const int ug::LagrangeP1< TRefElem >::dim = TRefElem::dim

static

Dimension, where shape functions are defined.

◆ nsh

template<typename TRefElem >

const size_t ug::LagrangeP1< TRefElem >::nsh = TRefElem::numCorners

static

Number of shape functions.

Referenced by ug::LagrangeP1< TRefElem >::num_sh().

◆ order

template<typename TRefElem >

const size_t ug::LagrangeP1< TRefElem >::order = 1

static

Order of Shape functions.

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

ugbase/lib_disc/local_finite_element/lagrange/lagrangep1.h

Public Types

Public Member Functions

Static Public Attributes

Private Types

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ grad_type

◆ reference_element_type

◆ shape_type

Constructor & Destructor Documentation

◆ LagrangeP1()

Member Function Documentation

◆ continuous()

◆ grad()

◆ num_sh()

◆ position()

◆ shape()

Member Data Documentation

◆ dim

◆ nsh

◆ order