PQ1 bubble scheme

Control-volume finite element scheme based on P1/Q1 basis function with enrichment by a bubble function. More...

Description

An extension of the box method is obtained when enriching the trial space by a bubble function. While the box method is a control-volume finite element scheme with piecewise constant basis functions, the bubble scheme uses basis functions enriched by a bubble function. The scheme is introduced in [75].

Control volume partitioning for the box with bubble method (PQ1Bubble).

The additional degree of freedom at the element center is used to ensure stability, for example in the case of velocity spaces for the Stokes problem. An additional overlapping control volume is introduced for the element degree of freedom.

Files
file	discretization/pq1bubble/fvelementgeometry.hh
	Base class for the local finite volume geometry for the pq1bubble method This builds up the sub control volumes and sub control volume faces for an element.
file	discretization/pq1bubble/fvgridgeometry.hh
	Base class for the finite volume geometry vector for the pq1bubble method This builds up the sub control volumes and sub control volume faces for each element of the grid partition.
file	discretization/pq1bubble/geometryhelper.hh
	Helper class constructing the dual grid finite volume geometries for the cvfe discretizazion method.
file	pq1bubblefecache.hh
	A finite element cache for P1/Q1 function with bubble.
file	pq1bubblelocalfiniteelement.hh
	Evaluate P1/Q1 basis with bubble function.
file	discretization/pq1bubble/subcontrolvolume.hh
	the sub control volume for the cvfe scheme
file	discretization/pq1bubble/subcontrolvolumeface.hh
	Base class for a sub control volume face.

Classes
class	Dumux::PQ1BubbleFVElementGeometry< GG, enableGridGeometryCache >
	Base class for the finite volume geometry vector for pq1bubble models This builds up the sub control volumes and sub control volume faces for each element. More...
struct	Dumux::PQ1BubbleDefaultGridGeometryTraits< GridView, MapperTraits >
	The default traits for the pq1bubble finite volume grid geometry Defines the scv and scvf types and the mapper types. More...
class	Dumux::PQ1BubbleFVGridGeometry< Scalar, GV, enableCaching, Traits >
	Base class for the finite volume geometry vector for pq1bubble schemes This builds up the sub control volumes and sub control volume faces. More...
class	Dumux::PQ1BubbleGeometryHelper< GridView, ScvType, ScvfType >
	A class to create sub control volume and sub control volume face geometries per element. More...
struct	Dumux::PQ1BubbleDefaultScvGeometryTraits< GridView >
	Default traits class to be used for the sub-control volumes for the pq1bubble scheme. More...
class	Dumux::PQ1BubbleSubControlVolume< GridView, T >
	the sub control volume for the pq1bubble scheme More...
struct	Dumux::PQ1BubbleDefaultScvfGeometryTraits< GridView >
	Default traits class to be used for the sub-control volume faces for the cvfe scheme. More...
class	Dumux::PQ1BubbleSubControlVolumeFace< GV, T >
	Class for a sub control volume face in the cvfe method, i.e a part of the boundary of a sub control volume we compute fluxes on. We simply use the base class here. More...