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LagrangeFE example 2

In this exmple we test Lagrange finite element on Triangle 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=Triangle
character(len=*), parameter :: elemName="Triangle"
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" order=1 Total Basis=3

N(1)=+1−1y1−1x1N(1)=+1-1 y^1-1x^1 N(2)=+1x1N(2)=+1x^1 N(3)=+1y1N(3)=+1 y^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=6

N(1)=+1−3y1+2y2+4x1y1−3x1+2x2N(1)=+1-3 y^1+2 y^2+4x^1 y^1-3x^1+2x^2 N(2)=−1x1+2x2N(2)=-1x^1+2x^2 N(3)=−1y1+2y2N(3)=-1 y^1+2 y^2 N(4)=−4x1y1+4x1−4x2N(4)=-4x^1 y^1+4x^1-4x^2 N(5)=+4x1y1N(5)=+4x^1 y^1 N(6)=+4y1−4y2−4x1y1N(6)=+4 y^1-4 y^2-4x^1 y^1

!!! 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=10

N(1)=+1+9y2−5.5y1−4.5y3−13.5x1y2+18x1y1−5.5x1+9x2−13.5x2y1−4.5x3N(1)=+1+9 y^2-5.5 y^1-4.5 y^3-13.5x^1 y^2+18x^1 y^1-5.5x^1+9x^2-13.5x^2 y^1-4.5x^3 N(2)=+1x1−4.5x2+4.5x3N(2)=+1x^1-4.5x^2+4.5x^3 N(3)=−4.5y2+1y1+4.5y3N(3)=-4.5 y^2+1 y^1+4.5 y^3 N(4)=+13.5x1y2−22.5x1y1+9x1−22.5x2+27x2y1+13.5x3N(4)=+13.5x^1 y^2-22.5x^1 y^1+9x^1-22.5x^2+27x^2 y^1+13.5x^3 N(5)=+4.5x1y1−4.5x1+18x2−13.5x2y1−13.5x3N(5)=+4.5x^1 y^1-4.5x^1+18x^2-13.5x^2 y^1-13.5x^3 N(6)=−4.5x1y1+13.5x2y1N(6)=-4.5x^1 y^1+13.5x^2 y^1 N(7)=+13.5x1y2−4.5x1y1N(7)=+13.5x^1 y^2-4.5x^1 y^1 N(8)=+18y2−4.5y1−13.5y3−13.5x1y2+4.5x1y1N(8)=+18 y^2-4.5 y^1-13.5 y^3-13.5x^1 y^2+4.5x^1 y^1 N(9)=−22.5y2+9y1+13.5y3+27x1y2−22.5x1y1+13.5x2y1N(9)=-22.5 y^2+9 y^1+13.5 y^3+27x^1 y^2-22.5x^1 y^1+13.5x^2 y^1 N(10)=−27x1y2+27x1y1−27x2y1N(10)=-27x^1 y^2+27x^1 y^1-27x^2 y^1 
END PROGRAM main