Sine1D

title '1D Accuracy test - Sine'

select

    ngrid=10

    stages = 4

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

coordinates

    cartesian1

Variables

    u

definitions

    k = 1

    h = 0.1

    w=0.1

    rs = abs(x)/w

    u0 = sin(rs)/max(rs,1e-18)

    s = -dxx(u0)

equations

    div(K*grad(u)) +s = 0

boundaries

    Region 1

       start(-1)  point value(u)=u0

       line to (1)  point value(u)=u0

monitors

    elevation(u) from (-1) to (1)

plots

    elevation(u,u0) from (-1) to (1)

    elevation(u-u0) from (-1) to (1)

    elevation(-div(grad(u)),s) from (-1) to (1)

histories

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

end