LagrangeFE example 3

In this exmple we test Lagrange finite element on Quadrangle 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=Quadrangle
character(len=*), parameter :: elemName="Quadrangle"
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=4

$$N(1)=+0.25-0.25 y^1-0.25x^1+0.25x^1 y^1$$ $$N(2)=+0.25-0.25 y^1+0.25x^1-0.25x^1 y^1$$ $$N(3)=+0.25+0.25 y^1+0.25x^1+0.25x^1 y^1$$ $$N(4)=+0.25+0.25 y^1-0.25x^1-0.25x^1 y^1$$

!!! 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=9

$$N(1)=+0.25x^1 y^1-0.25x^1 y^2-0.25x^2 y^1+0.25x^2 y^2$$ $$N(2)=-0.25x^1 y^1+0.25x^1 y^2-0.25x^2 y^1+0.25x^2 y^2$$ $$N(3)=+0.25x^1 y^1+0.25x^1 y^2+0.25x^2 y^1+0.25x^2 y^2$$ $$N(4)=-0.25x^1 y^1-0.25x^1 y^2+0.25x^2 y^1+0.25x^2 y^2$$ $$N(5)=+0.5 y^2-0.5 y^1+0.5x^2 y^1-0.5x^2 y^2$$ $$N(6)=+0.5x^1-0.5x^1 y^2+0.5x^2-0.5x^2 y^2$$ $$N(7)=+0.5 y^2+0.5 y^1-0.5x^2 y^1-0.5x^2 y^2$$ $$N(8)=-0.5x^1+0.5x^1 y^2+0.5x^2-0.5x^2 y^2$$ $$N(9)=+1-1 y^2-1x^2+1x^2 y^2$$

!!! 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) )

END PROGRAM main