<< Click to Display Table of Contents >> constraint 

{ CONSTRAINT.PDE
This problem shows the use of CONSTRAINTS to resolve an illposed problem.
There are no value boundary conditions in any of the three equations, so
there are infinitely many solutions that satisfy the PDE's. The constraints
select from the family of solutions those which have a mean value of 1.
}
title 'Constraint Test'
variables
u1 u2 u3
equations
u1: div(grad(u1)) +x = 0
u2: div(grad(u2)) +x+y = 0
u3: div(grad(u3)) +y = 0
constraints
integral(u1) = integral(1)
integral(u2) = integral(1)
integral(u3) = integral(1)
boundaries
Region 1
start(1,1) line to (1,1) to (1,1) to (1,1) to close
monitors
contour(u1)
contour(u2)
contour(u3)
plots
contour(u1) report(integral(u1)/integral(1)) as "Average"
contour(u2) report(integral(u2)/integral(1)) as "Average"
contour(u3) report(integral(u3)/integral(1)) as "Average"
surface(u1) report(integral(u1)/integral(1)) as "Average"
surface(u2) report(integral(u2)/integral(1)) as "Average"
surface(u3) report(integral(u3)/integral(1)) as "Average"
end