Discretization schemes

The discretization schemes available in DuMu^x More...

Description

Modules
	Cell-centered Finite Volume Methods
	Finite volume schemes with degrees of freedom located at grid cell centers.
	Control-volume Finite Element Methods
	Control-volume finite element schemes (e.g. box method) Control-volume finite element schemes are based on finite element basis functions for interpolation but define control volumes to construct a finite volume scheme. They can be interpreted both as finite volume or as (Petrov-Galerkin) finite element scheme.
	Staggered Grid Finite Volume Method
	Discretization for the momentum balance of the Navier-Stokes equations. Can be used to build a marker-and-cell scheme (MAC) together with Tpfa for the discretization of the mass balance equation.
	Staggered FV scheme
	A staggered finite volume scheme with degrees of freedom at cell-centers and facets. In this implementation, momentum control volumes do not explicitly exist, but the implementation uses workarounds.
	Finite Element Methods
	The finite element method.
	Pore-network Models
	The pore-network model discretization.

Files
file	basegridgeometry.hh
	Base class for grid geometries.
file	basicgridgeometry.hh
	A basic implementation of a grid geometry with some common interfaces.
file	box.hh
	Defines a type tag and some properties for models using the box scheme.
file	ccmpfa.hh
	Properties for all models using cell-centered finite volume scheme with mpfa.
file	cctpfa.hh
	Properties for all models using cell-centered finite volume scheme with TPFA.
file	checkoverlapsize.hh
	Check the overlap size for different discretization methods.
file	elementsolution.hh
	Element solution classes and factory functions.
file	evalgradients.hh
	free functions for the evaluation of primary variable gradients inside elements.
file	evalsolution.hh
	free functions for the evaluation of primary variables inside elements.
file	extrusion.hh
	Helper classes to compute the integration elements.
file	fcdiamond.hh
	Defines a type tag and some properties for models using the diamond scheme. This scheme features degrees of freedom at the elements' centers and intersections (faces).
file	fcstaggered.hh
	Defines a type tag and some properties for models using the staggered scheme. This scheme features degrees of freedom at the elements' centers and intersections (faces). TODO: detailed documentation and figures.
file	fluxstencil.hh
	The flux stencil specialized for different discretization schemes.
file	functionspacebasis.hh
	Provides helper aliases and functionality to obtain the types and instances of Dune::Functions function space bases that underlie different discretization schemes.
file	discretization/fvgridvariables.hh
	The grid variable class for finite volume schemes, storing variables on scv and scvf (volume and flux variables)
file	fvproperties.hh
	Declares properties required for finite-volume models models.
file	localdoftraits.hh
	Element-specific traits of grid geometries / discretization schemes.
file	localview.hh
	Free function to get the local view of a grid cache object.
file	method.hh
	The available discretization methods in Dumux.
file	nonconformingfecache.hh
	A finite element cache for the non-conforming FE spaces RT and CR.
file	pq1bubble.hh
	Defines a type tag and some properties for models using the pq1bubble scheme.
file	l2_projection.hh
	L2-projections of analytic functions into a given function space.
file	projector.hh
	Contains functionality for L2-projections from one function space into another, which can live both on the same or different grids of potentially different dimensionality.
file	scvandscvfiterators.hh
	Class providing iterators over sub control volumes and sub control volume faces of an element.
file	staggered.hh
	Defines a type tag and some properties for models using the staggered scheme. This scheme features degrees of freedom at the elements' centers and intersections (faces). TODO: detailed documentation and figures.
file	subcontrolvolumebase.hh
	Base class for a sub control volume.
file	subcontrolvolumefacebase.hh
	Base class for a sub control volume face.
file	walldistance.hh
file	experimental/discretization/fvgridvariables.hh
	The grid variable class for finite volume schemes, storing variables on scv and scvf (volume and flux variables)
file	experimental/discretization/gridvariables.hh
	Base class for grid variables.

Classes
class	Dumux::BaseGridGeometry< GV, Traits >
	Base class for all grid geometries. More...
class	Dumux::BasicGridGeometry< GV, EM, VM >
	An implementation of a grid geometry with some basic features. More...
struct	Dumux::CheckOverlapSize< DiscretizationMethod >
	Check if the overlap size is valid for a given discretization method. More...
struct	Dumux::NoExtrusion
	Default implementation that performs no extrusion (extrusion with identity) More...
struct	Dumux::RotationalExtrusion< radAx >
	Rotation symmetric extrusion policy for rotating about an external axis. More...
struct	Dumux::SphericalExtrusion
	Rotation symmetric extrusion policy for spherical rotation. More...
class	Dumux::FluxStencil< FVElementGeometry, DiscretizationMethod >
	The flux stencil specialized for different discretization schemes. More...
class	Dumux::FVGridVariables< GG, GVV, GFVC >
	The grid variable class for finite volume schemes storing variables on scv and scvf (volume and flux variables) More...
class	Dumux::Projector< ScalarType >
	Does an L2-projection from one discrete function space into another. The convenience functions makeProjectorPair or makeProjector can be used to create such a projection. More...
class	Dumux::ScvIterator< SubControlVolume, Vector, FVElementGeometry >
	Iterators over sub control volumes. More...
class	Dumux::ScvfIterator< SubControlVolumeFace, Vector, FVElementGeometry >
	Iterators over sub control volume faces of an fv geometry. More...
class	Dumux::SkippingScvfIterator< SubControlVolumeFace, Vector, FVElementGeometry >
	Iterators over sub control volume faces of an fv geometry and a given sub control volume. More...
class	Dumux::SubControlVolumeBase< Imp, ScvGeometryTraits >
	Base class for a sub control volume, i.e a part of the control volume we are making the balance for. Defines the general interface. More...
class	Dumux::SubControlVolumeFaceBase< Imp, ScvfGeometryTraits >
	Base class for a sub control volume face, i.e a part of the boundary of a sub control volume we computing a flux on. More...
class	Dumux::WallDistance< GridGeometry, DistanceField >
	Class to calculate the wall distance at every element or vertex of a grid. More...
class	Dumux::Experimental::FVGridVariablesLocalView< GV >
	Finite volume-specific local view on grid variables. More...
class	Dumux::Experimental::FVGridVariables< GVV, GFVC, X >
	The grid variable class for finite volume schemes, storing variables on scv and scvf (volume and flux variables). More...
class	Dumux::Experimental::GridVariables< GG, X >
	Base class for grid variables. More...

Typedefs
template<class GV , class T >
using	Dumux::BasicGridGeometry_t = Dune::Std::detected_or_t< Dumux::BasicGridGeometry< GV, typename T::ElementMapper, typename T::VertexMapper >, Detail::SpecifiesBaseGridGeometry, T >
	Type of the basic grid geometry implementation used as backend. More...

Functions
	Dumux::BaseGridGeometry< GV, Traits >::BaseGridGeometry (std::shared_ptr< BaseImplementation > impl)
	Constructor from a BaseImplementation. More...
	Dumux::BaseGridGeometry< GV, Traits >::BaseGridGeometry (const GridView &gridView)
	Constructor from a grid view. More...
	Dumux::BasicGridGeometry< GV, EM, VM >::BasicGridGeometry (const GridView &gridView)
	Constructor computes the bounding box of the entire domain, for e.g. setting boundary conditions. More...
template<class Element , class SolutionVector , class GridGeometry >
auto	Dumux::elementSolution (const Element &element, const SolutionVector &sol, const GridGeometry &gg) -> std::enable_if_t< GridGeometry::discMethod==DiscretizationMethods::cctpfa||GridGeometry::discMethod==DiscretizationMethods::ccmpfa, CCElementSolution< typename GridGeometry::LocalView, std::decay_t< decltype(std::declval< SolutionVector >()[0])> > >
	Make an element solution for cell-centered schemes. More...
template<class Element , class ElementVolumeVariables , class FVElementGeometry >
auto	Dumux::elementSolution (const Element &element, const ElementVolumeVariables &elemVolVars, const FVElementGeometry &gg) -> std::enable_if_t< FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::cctpfa||FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::ccmpfa, CCElementSolution< FVElementGeometry, typename ElementVolumeVariables::VolumeVariables::PrimaryVariables > >
	Make an element solution for cell-centered schemes. More...
template<class FVElementGeometry , class PrimaryVariables >
auto	Dumux::elementSolution (PrimaryVariables &&priVars) -> std::enable_if_t< FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::cctpfa||FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::ccmpfa, CCElementSolution< FVElementGeometry, PrimaryVariables > >
	Make an element solution for cell-centered schemes. More...
template<class FVElementGeometry , class PrimaryVariables >
auto	Dumux::elementSolution (const PrimaryVariables &priVars) -> std::enable_if_t< FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::cctpfa||FVElementGeometry::GridGeometry::discMethod==DiscretizationMethods::ccmpfa, CCElementSolution< FVElementGeometry, PrimaryVariables > >
	Make an element solution for cell-centered schemes. More...
template<class Element , class GridGeometry , class CVFEElemSol >
auto	Dumux::Detail::evalCVFEGradients (const Element &element, const typename Element::Geometry &geometry, const GridGeometry &gridGeometry, const CVFEElemSol &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Evaluates the gradient of a control-volume finite element solution to a given global position. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
auto	Dumux::evalGradients (const Element &element, const typename Element::Geometry &geometry, const typename FVElementGeometry::GridGeometry &gridGeometry, const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Evaluates the gradient of a given CVFE element solution to a given global position. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
Dune::FieldVector< typename Element::Geometry::GlobalCoordinate, PrimaryVariables::dimension >	Dumux::evalGradients (const Element &element, const typename Element::Geometry &geometry, const typename FVElementGeometry::GridGeometry &gridGeometry, const CCElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos)
	Evaluates the gradient of a given CCElementSolution to a given global position. This function is only here for (compilation) compatibility reasons with the box scheme. The solution within the control volumes is constant and thus gradients are zero. One can compute gradients towards the sub-control volume faces after reconstructing the solution on the faces. More...
template<class Element , class GridGeometry , class CVFEElemSol >
CVFEElemSol::PrimaryVariables	Dumux::Detail::evalCVFESolution (const Element &element, const typename Element::Geometry &geometry, const GridGeometry &gridGeometry, const CVFEElemSol &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Interpolates a given control-volume finite element solution at a given global position. Uses the finite element cache of the grid geometry. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
PrimaryVariables	Dumux::evalSolution (const Element &element, const typename Element::Geometry &geometry, const typename FVElementGeometry::GridGeometry &gridGeometry, const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Interpolates a given box element solution at a given global position. Uses the finite element cache of the grid geometry. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
PrimaryVariables	Dumux::evalSolution (const Element &element, const typename Element::Geometry &geometry, const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Interpolates a given box element solution at a given global position. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
PrimaryVariables	Dumux::evalSolution (const Element &element, const typename Element::Geometry &geometry, const typename FVElementGeometry::GridGeometry &gridGeometry, const CCElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Interpolates a given cell-centered element solution at a given global position. More...
template<class Element , class FVElementGeometry , class PrimaryVariables >
PrimaryVariables	Dumux::evalSolution (const Element &element, const typename Element::Geometry &geometry, const CCElementSolution< FVElementGeometry, PrimaryVariables > &elemSol, const typename Element::Geometry::GlobalCoordinate &globalPos, bool ignoreState=false)
	Interpolates a given cell-centered element solution at a given global position. Overload of the above evalSolution() function without a given gridGeometry. For compatibility reasons with the box scheme. More...
template<class GridCache >
GridCache::LocalView	Dumux::localView (const GridCache &gridCache)
	Free function to get the local view of a grid cache object. More...
template<class FEBasisDomain , class FEBasisTarget , class GlueType >
auto	Dumux::makeProjectorPair (const FEBasisDomain &feBasisDomain, const FEBasisTarget &feBasisTarget, GlueType glue)
	Creates a pair of projectors between the space with basis feBasisDomain to the space with basis feBasisTarget. More...
template<class FEBasisDomain , class FEBasisTarget , class GlueType >
auto	Dumux::makeProjector (const FEBasisDomain &feBasisDomain, const FEBasisTarget &feBasisTarget, GlueType glue)
	Creates a forward projector from the space feBasisDomain to the space with basis feBasisTarget. More...
template<class PrimaryVariables , class CellCenterPrimaryVariables >
StaggeredElementSolution< PrimaryVariables >	Dumux::makeElementSolutionFromCellCenterPrivars (const CellCenterPrimaryVariables &cellCenterPriVars)
	Helper function to create an elementSolution from cell center primary variables. More...

Typedef Documentation

BasicGridGeometry_t

template<class GV , class T >

using Dumux::BasicGridGeometry_t = typedef Dune::Std::detected_or_t< Dumux::BasicGridGeometry<GV, typename T::ElementMapper, typename T::VertexMapper>, Detail::SpecifiesBaseGridGeometry, T >

Function Documentation

BaseGridGeometry() [1/2]

template<class GV , class Traits >

Dumux::BaseGridGeometry< GV, Traits >::BaseGridGeometry ( const GridView &  gridView )

inline

Parameters

gridView

the grid view on which to construct the grid geometry

BaseGridGeometry() [2/2]

template<class GV , class Traits >

Dumux::BaseGridGeometry< GV, Traits >::BaseGridGeometry ( std::shared_ptr< BaseImplementation >  impl )

inline

BasicGridGeometry()

template<class GV , class EM , class VM >

Dumux::BasicGridGeometry< GV, EM, VM >::BasicGridGeometry ( const GridView &  gridView )

inline

Parameters

gridView

the grid view on which to construct the grid geometry

elementSolution() [1/4]

template<class Element , class ElementVolumeVariables , class FVElementGeometry >

auto Dumux::elementSolution	(	const Element &	element,
		const ElementVolumeVariables &	elemVolVars,
		const FVElementGeometry &	gg
	)		-> std::enable_if_t<FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::cctpfa || FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::ccmpfa, CCElementSolution<FVElementGeometry, typename ElementVolumeVariables::VolumeVariables::PrimaryVariables>>

Make an element solution for face-centered staggered schemes.

Make an element solution for control-volume finite element schemes.

elementSolution() [2/4]

template<class Element , class SolutionVector , class GridGeometry >

auto Dumux::elementSolution	(	const Element &	element,
		const SolutionVector &	sol,
		const GridGeometry &	gg
	)		-> std::enable_if_t<GridGeometry::discMethod == DiscretizationMethods::cctpfa || GridGeometry::discMethod == DiscretizationMethods::ccmpfa, CCElementSolution<typename GridGeometry::LocalView, std::decay_t<decltype(std::declval<SolutionVector>()[0])>> >

Make an element solution for face-centered staggered schemes.

Make an element solution for control-volume finite element schemes.

elementSolution() [3/4]

template<class FVElementGeometry , class PrimaryVariables >

auto Dumux::elementSolution

(

const PrimaryVariables &

priVars

)

-> std::enable_if_t<FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::cctpfa || FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::ccmpfa, CCElementSolution<FVElementGeometry, PrimaryVariables>>

Note

This is e.g. used to construct an element solution at Dirichlet boundaries

elementSolution() [4/4]

template<class FVElementGeometry , class PrimaryVariables >

auto Dumux::elementSolution

(

PrimaryVariables &&

priVars

)

-> std::enable_if_t<FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::cctpfa || FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::ccmpfa, CCElementSolution<FVElementGeometry, PrimaryVariables>>

Make an element solution for staggered schemes.

Make an element solution for face-centered staggered schemes.

Note

This is e.g. used to construct an element solution at Dirichlet boundaries

evalCVFEGradients()

template<class Element , class GridGeometry , class CVFEElemSol >

auto Dumux::Detail::evalCVFEGradients	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const GridGeometry &	gridGeometry,
		const CVFEElemSol &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

Returns

Dune::FieldVector with as many entries as dimension of the PrimaryVariables object (i.e. numEq). Each entry is a GlobalCoordinate object holding the priVar gradient.

evalCVFESolution()

template<class Element , class GridGeometry , class CVFEElemSol >

CVFEElemSol::PrimaryVariables Dumux::Detail::evalCVFESolution	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const GridGeometry &	gridGeometry,
		const CVFEElemSol &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Returns

the interpolated primary variables

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

evalGradients() [1/2]

template<class Element , class FVElementGeometry , class PrimaryVariables >

Dune::FieldVector< typename Element::Geometry::GlobalCoordinate, PrimaryVariables::dimension > Dumux::evalGradients	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const typename FVElementGeometry::GridGeometry &	gridGeometry,
		const CCElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos
	)

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position

Exceptions

Dune::NotImplemented

Returns

Dune::FieldVector with as many entries as dimension of the PrimaryVariables object (i.e. numEq). Each entry is a GlobalCoordinate object holding the priVar gradient.

evalGradients() [2/2]

template<class Element , class FVElementGeometry , class PrimaryVariables >

auto Dumux::evalGradients	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const typename FVElementGeometry::GridGeometry &	gridGeometry,
		const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

evalSolution() [1/4]

template<class Element , class FVElementGeometry , class PrimaryVariables >

PrimaryVariables Dumux::evalSolution	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const CCElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Returns

the primary variables (constant over the element)

Parameters

element	The element
geometry	The element geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

evalSolution() [2/4]

template<class Element , class FVElementGeometry , class PrimaryVariables >

PrimaryVariables Dumux::evalSolution	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Overload of the above evalSolution() function without a given gridGeometry. The local basis is computed on the fly.

Returns

the interpolated primary variables

Parameters

element	The element
geometry	The element geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

evalSolution() [3/4]

template<class Element , class FVElementGeometry , class PrimaryVariables >

PrimaryVariables Dumux::evalSolution	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const typename FVElementGeometry::GridGeometry &	gridGeometry,
		const CCElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Returns

the primary variables (constant over the element)

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

evalSolution() [4/4]

template<class Element , class FVElementGeometry , class PrimaryVariables >

PrimaryVariables Dumux::evalSolution	(	const Element &	element,
		const typename Element::Geometry &	geometry,
		const typename FVElementGeometry::GridGeometry &	gridGeometry,
		const CVFEElementSolution< FVElementGeometry, PrimaryVariables > &	elemSol,
		const typename Element::Geometry::GlobalCoordinate &	globalPos,
		bool	ignoreState = false
	)

Returns

the interpolated primary variables

Parameters

element	The element
geometry	The element geometry
gridGeometry	The finite volume grid geometry
elemSol	The primary variables at the dofs of the element
globalPos	The global position
ignoreState	If true, the state of primary variables is ignored

localView()

template<class GridCache >

GridCache::LocalView Dumux::localView ( const GridCache &  gridCache )

inline

Note

A local object is only functional after calling its bind/bindElement method.

Template Parameters

GridCache

the grid caching type (such as GridGeometry)

Parameters

gridCache

the grid caching object we want to localView from

makeElementSolutionFromCellCenterPrivars()

template<class PrimaryVariables , class CellCenterPrimaryVariables >

StaggeredElementSolution< PrimaryVariables > Dumux::makeElementSolutionFromCellCenterPrivars

(

const CellCenterPrimaryVariables &

cellCenterPriVars

)

Template Parameters

PrimaryVariables	The type of the desired primary variables object
CellCenterPrimaryVariables	The type of the cell center (input) primary variables object

Parameters

cellCenterPriVars

The cell center (input) primary variables object

makeProjector()

template<class FEBasisDomain , class FEBasisTarget , class GlueType >

auto Dumux::makeProjector	(	const FEBasisDomain &	feBasisDomain,
		const FEBasisTarget &	feBasisTarget,
		GlueType	glue
	)

Parameters

feBasisDomain	The domain finite element space basis
feBasisTarget	The target finite element space basis
glue	The glue object containing the intersections between the grids.

Returns

The forward projector from the space with basis feBasisDomain to the space with basis feBasisTarget.

makeProjectorPair()

template<class FEBasisDomain , class FEBasisTarget , class GlueType >

auto Dumux::makeProjectorPair	(	const FEBasisDomain &	feBasisDomain,
		const FEBasisTarget &	feBasisTarget,
		GlueType	glue
	)

Parameters

feBasisDomain	The domain finite element space basis
feBasisTarget	The target finite element space basis
glue	The glue object containing the intersections between the grids.

Returns

An std::pair of projectors where the first is the forward projector from the space with basis feBasisDomain to the space with basis feBasisTarget and the second does the backward projection.