Sine2D

title '2D Accuracy Test - Sine'

select

    stages = 4

    errlim = staged(1e-2, 1e-3, 1e-4, 1e-5)

Variables

    u

definitions

    k = 1

    h = 0.1

    w=0.1

    rs = r/w

    u0 = sin(rs)/rs

    s = -dxx(u0)-dyy(u0)

!Initial values

    !u = u0

equations

    div(K*grad(u)) +s = 0

boundaries

    Region 1

       start(-1,-1)  value(u)=u0

line to (1,-1) to (1,1) to (-1,1) to close

monitors

    grid(x,y)

    contour(u)

plots

    grid(x,y)

    contour(u)

    elevation(u,u0) from(-1,0) to (1,0)

    elevation(u-u0) from(-1,0) to (1,0)

    elevation(dxx(u),dxx(u0),s) from(-1,0) to (1,0)

    contour(dxx(u)) contour(dxy(u)) contour(dyy(u))

histories

    history(sqrt(integral((u-u0)^2)/integral(1)), errlim)

end