projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider Class Reference

Element matrix provider for the stokes system. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/ipdg_stokes/assemble/piecewise_const_element_matrix_provider.h>

Public Member Functions
	PiecewiseConstElementMatrixProvider (double sigma, const lf::mesh::utils::MeshDataSet< bool > &boundary, bool modified=false)
	Constructor. More...
Eigen::MatrixXd	Eval (const lf::mesh::Entity &entity) const
	Compute the element matrix for some entity of a mesh. More...
bool	isActive (const lf::mesh::Entity &entity) const
	All entities are regarded as active. More...

Private Attributes
const double	sigma_
const lf::mesh::utils::MeshDataSet< bool > &	boundary_
const bool	modified_

Detailed Description

Element matrix provider for the stokes system.

As basis functions, the curl of the standard linear Lagrangian FEM hat functions is used in order to guarantee divergence-freeness of the solution.

Note

Currently, only triangular meshes are supported

The (global) bilinear form is given by

\[ (u, v) \mapsto \sum_{e \in \mathcal{E}(\mathcal{M})} \int_e\! \frac{\sigma}{|e|}\left[\!\left[ u \cdot \tau_e \right]\!\right] : \left[\!\left[ v \cdot \tau_e \right]\!\right] \,\mathrm{d}x \]

To enable local assembly of the system matrix, auxilary dofs are introduced on the edges of the mesh which are then forced to be equal to the jump of \(u\) over that edge. As we use Raviart-Thomas basis functions, the normal component of the function is continuous over the mesh edges. For this reason, the jump terms only consist of the jump in the tangential direction over an edge.

Definition at line 39 of file piecewise_const_element_matrix_provider.h.

Constructor & Destructor Documentation

PiecewiseConstElementMatrixProvider()

projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::PiecewiseConstElementMatrixProvider	(	double	sigma,
		const lf::mesh::utils::MeshDataSet< bool > &	boundary,
		bool	modified = false
	)

Constructor.

Parameters

sigma	The stabilization coefficient of the IPDG method
boundary	A MeshDataSet marking the boundary edges
modified	If true, the modified penalty term is used missing the scaling with 1/|e_n|

Definition at line 12 of file piecewise_const_element_matrix_provider.cc.

Member Function Documentation

Eval()

Eigen::MatrixXd projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::Eval

(

const lf::mesh::Entity &

entity

)

const

Compute the element matrix for some entity of a mesh.

Parameters

entity

The mesh entity to compute the element matrix for

Returns

The 6 by 6 element matrix of the given entity

Note

This function only works for triangles

Definition at line 17 of file piecewise_const_element_matrix_provider.cc.

References boundary_, projects::ipdg_stokes::mesh::computeOutwardNormals(), lf::mesh::Entity::Geometry(), lf::geometry::Geometry::Global(), lf::uscalfe::FeLagrangeO1Tria< SCALAR >::GradientsReferenceShapeFunctions(), modified_, lf::base::RefEl::NodeCoords(), lf::mesh::Entity::RefEl(), sigma_, lf::mesh::Entity::SubEntities(), and lf::geometry::Volume().

isActive()

bool projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::isActive ( const lf::mesh::Entity &  entity ) const

inline

All entities are regarded as active.

Definition at line 64 of file piecewise_const_element_matrix_provider.h.

Member Data Documentation

boundary_

const lf::mesh::utils::MeshDataSet<bool>& projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::boundary_

private

Definition at line 68 of file piecewise_const_element_matrix_provider.h.

Referenced by Eval().

modified_

const bool projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::modified_

private

Definition at line 69 of file piecewise_const_element_matrix_provider.h.

Referenced by Eval().

sigma_

const double projects::ipdg_stokes::assemble::PiecewiseConstElementMatrixProvider::sigma_

private

Definition at line 67 of file piecewise_const_element_matrix_provider.h.

Referenced by Eval().

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

• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/ipdg_stokes/assemble/piecewise_const_element_matrix_provider.h
• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/ipdg_stokes/assemble/piecewise_const_element_matrix_provider.cc