Solve Poisson equation with integral constraint

NGSolve
1

Hi!

I am working on solving a PDE using an integral constraint. For example, let’s say we want to solve the Poisson equation

\Delta u=C\text{ in }\Omega,
u=0\text{ on }\partial\Omega,

where C is constant in \Omega, with the integral constraint

\int_\Omega u\mathrm{d}\Omega = 1.

To satisfy this constraint, I would like to use the constant C as a variable.

Is this type of problem possible to solve in ngsolve? I’ve tried using ngsolve.Integrate inside the bilinear form but that seems to be impossible.

Thanks!

Cas

2

You can use NumberSpace (which is one constant function on the whole domain) to enforce mean-value constraints, find an example here:
https://docu.ngsolve.org/ngs24/tutorials/13_nonlinear.html#another-example-stationary-navier-stokes

3

Thanks a lot for the quick reply! The NumberSpace works wonders.