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

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

!!! 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

$$N(1)=+1-3 y^1+2 y^2+4x^1 y^1-3x^1+2x^2$$ $$N(2)=-1x^1+2x^2$$ $$N(3)=-1 y^1+2 y^2$$ $$N(4)=-4x^1 y^1+4x^1-4x^2$$ $$N(5)=+4x^1 y^1$$ $$N(6)=+4 y^1-4 y^2-4x^1 y^1$$

!!! 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

$$N(1)=+1+9 y^2-5.5 y^1-4.5 y^3-13.5x^1 y^2+18x^1 y^1-5.5x^1+9x^2-13.5x^2 y^1-4.5x^3$$ $$N(2)=+1x^1-4.5x^2+4.5x^3$$ $$N(3)=-4.5 y^2+1 y^1+4.5 y^3$$ $$N(4)=+13.5x^1 y^2-22.5x^1 y^1+9x^1-22.5x^2+27x^2 y^1+13.5x^3$$ $$N(5)=+4.5x^1 y^1-4.5x^1+18x^2-13.5x^2 y^1-13.5x^3$$ $$N(6)=-4.5x^1 y^1+13.5x^2 y^1$$ $$N(7)=+13.5x^1 y^2-4.5x^1 y^1$$ $$N(8)=+18 y^2-4.5 y^1-13.5 y^3-13.5x^1 y^2+4.5x^1 y^1$$ $$N(9)=-22.5 y^2+9 y^1+13.5 y^3+27x^1 y^2-22.5x^1 y^1+13.5x^2 y^1$$ $$N(10)=-27x^1 y^2+27x^1 y^1-27x^2 y^1$$

END PROGRAM main