Special "named" quadrature rules

Detailed Description

Creation of special quadrature rules.

These functions provide a number of special quadrature rules in the forms of QuadRule objects. They are meant to be used in low-order finite element methods when the quadrature rules can easily fixed a-priori and should feature a special location of quadrature points as is required, e.g., for mass-lumping techniques.

For some examples see Lecture Document Example 2.7.5.33.

QuadRule objects with a particular order but otherwise unspecified properties can be created by lf::quad::make_QuadRule().

Functions
QuadRule	lf::quad::make_TriaQR_MidpointRule ()
	midpoint quadrature rule for triangles
QuadRule	lf::quad::make_TriaQR_P1O2 ()
QuadRule	lf::quad::make_TriaQR_EdgeMidpointRule ()
	edge midpoint quadrature rule for reference triangles
QuadRule	lf::quad::make_TriaQR_P3O3 ()
QuadRule	lf::quad::make_TriaQR_P7O6 ()
	Seven point triangular quadrature rule of order 6.
QuadRule	lf::quad::make_TriaQR_P6O4 ()
	Six point triangular quadrature rule of order 4.
QuadRule	lf::quad::make_QuadQR_MidpointRule ()
	midpoint quadrature rule for quadrilaterals
QuadRule	lf::quad::make_QuadQR_P1O2 ()
QuadRule	lf::quad::make_QuadQR_EdgeMidpointRule ()
	edge midpoint quadrature rule for unit square (= reference quad)
QuadRule	lf::quad::make_QuadQR_P4O2 ()
QuadRule	lf::quad::make_QuadQR_P4O4 ()
	Fourth-order tensor product Gauss rule for quadrilaterals.

Function Documentation

make_QuadQR_EdgeMidpointRule()

QuadRule lf::quad::make_QuadQR_EdgeMidpointRule

(

)

edge midpoint quadrature rule for unit square (= reference quad)

This quadrature rule relies on point evaluations at the midpoints of all edges with equal weights = 1/4 for the unit square.

The rule is exact for bilinear polynomials.

Definition at line 191 of file make_quad_rule.cc.

References lf::base::RefEl::kQuad().

Referenced by lf::quad::make_QuadQR_P4O2().

make_QuadQR_MidpointRule()

QuadRule lf::quad::make_QuadQR_MidpointRule ( )

inline

midpoint quadrature rule for quadrilaterals

This quadrature rule relies on the center of gravity as single quadrature node. It agrees with the lowest-order tensor product Gauss rule

Definition at line 79 of file make_quad_rule.h.

References lf::base::RefEl::kQuad(), and lf::quad::make_QuadRule().

Referenced by lf::quad::make_QuadQR_P1O2().

make_QuadQR_P1O2()

QuadRule lf::quad::make_QuadQR_P1O2 ( )

inline

Definition at line 82 of file make_quad_rule.h.

References lf::quad::make_QuadQR_MidpointRule().

make_QuadQR_P4O2()

QuadRule lf::quad::make_QuadQR_P4O2 ( )

inline

Definition at line 92 of file make_quad_rule.h.

References lf::quad::make_QuadQR_EdgeMidpointRule().

make_QuadQR_P4O4()

QuadRule lf::quad::make_QuadQR_P4O4 ( )

inline

Fourth-order tensor product Gauss rule for quadrilaterals.

Rule uses four interior quadrature nodes and is exact for tensor-product polynomials up to degree 3.

Definition at line 99 of file make_quad_rule.h.

References lf::base::RefEl::kQuad(), and lf::quad::make_QuadRule().

make_TriaQR_EdgeMidpointRule()

QuadRule lf::quad::make_TriaQR_EdgeMidpointRule

(

)

edge midpoint quadrature rule for reference triangles

This quadrature rule relies on point evaluations at the midpoints of all edges with equal weights = 1/6 for the reference triangle.

The rule is exact for quadratic bi-variate polynomials

Definition at line 172 of file make_quad_rule.cc.

References lf::base::RefEl::kTria().

Referenced by lf::quad::make_TriaQR_P3O3().

make_TriaQR_MidpointRule()

QuadRule lf::quad::make_TriaQR_MidpointRule

(

)

midpoint quadrature rule for triangles

This quadrature rule relies on the center of gravity as single quadrature node

Definition at line 159 of file make_quad_rule.cc.

References lf::base::RefEl::kTria().

Referenced by lf::quad::make_TriaQR_P1O2().

make_TriaQR_P1O2()

QuadRule lf::quad::make_TriaQR_P1O2 ( )

inline

Definition at line 56 of file make_quad_rule.h.

References lf::quad::make_TriaQR_MidpointRule().

make_TriaQR_P3O3()

QuadRule lf::quad::make_TriaQR_P3O3 ( )

inline

Definition at line 66 of file make_quad_rule.h.

References lf::quad::make_TriaQR_EdgeMidpointRule().

make_TriaQR_P6O4()

QuadRule lf::quad::make_TriaQR_P6O4

(

)

Six point triangular quadrature rule of order 4.

Definition at line 213 of file make_quad_rule.cc.

References lf::base::RefEl::kTria().

make_TriaQR_P7O6()

QuadRule lf::quad::make_TriaQR_P7O6

(

)

Seven point triangular quadrature rule of order 6.

Definition at line 237 of file make_quad_rule.cc.