Gaus2D

title '2D Accuracy Test - Gaussian'

Variables

    u

select

    stages = 4

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

definitions

    k = 1

    h = 0.1

    w=0.1    ! gaussian width

    u0 = exp(-(x^2+y^2)/w^2)

    s = -[dxx(u0)+dyy(u0)]

equations

    div(K*grad(u)) +s = 0

boundaries

    Region 1

       start(-1,-1)  natural(u)=0 line to (1,-1)

       value(u)=u0 line to (1,1)

       natural(u)=0  line to (-1,1)

       value(u) = u0 line 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