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