LagrangeFE example 1

In this exmple we test Lagrange finite element on Line element. Interpolation points are equidistance.

Modules and classes

• [[LagrangeFE_]]

Usage

PROGRAM main
use easifemBase
use easifemClasses
implicit none
type(LagrangeFE_) :: obj
integer(i4b) :: order
integer(i4b), parameter :: elemType=Line
character(len=*), parameter :: elemName="Line"
integer(i4b), parameter :: ipType=IP_EQUIDISTANCE

!!! note "Order=1"

  order=1
  call obj%Initiate(elemType=elemType, order=order, ipType=ipType)
  call obj%Display( elemName // "order=" //tostring(order) )

!!! example "result"

ReferenceElement=
element type : Line2
xidimension :: 1
nsd : 1
nsd=1
order=1
feType=1
ipType=1
dofType=
--------
1
1
1
1
transformType=1

order=1
Total Basis=2
N(1)=+0.5x^0-0.5x^1
N(2)=+0.5x^0+0.5x^1

$$N(1)=+0.5x^0-0.5x^1$$ $$N(2)=+0.5x^0+0.5x^1$$

!!! note "Order=2"

  order=2
  call blanklines(nol=3)
  call obj%Initiate(elemType=elemType, order=order, ipType=ipType)
  call obj%Display( elemName // "order=" //tostring(order) )

!!! example "result"

order=2 Total Basis=3

$$N(1)=-0.5x^1+0.5x^2$$ $$N(2)=+0.5x^1+0.5x^2$$ $$N(3)=+1x^0-1x^2$$

!!! note "Order=3"

  order=3
  call blanklines(nol=3)
  call obj%Initiate(elemType=elemType, order=order, ipType=ipType)
  call obj%Display( elemName // "order=" //tostring(order) )

!!! example "result" order=3 Total Basis=4

$$N(1)=-6.25E-02x^0+6.25E-02x^1+0.5625x^2-0.5625x^3$$ $$N(2)=-6.25E-02x^0-6.25E-02x^1+0.5625x^2+0.5625x^3$$ $$N(3)=+0.5625x^0-1.6875x^1-0.5625x^2+1.6875x^3$$ $$N(4)=+0.5625x^0+1.6875x^1-0.5625x^2-1.6875x^3$$

END PROGRAM main