I am trying to simulate a planar, high ohmic DC gas-discharge system. The model consists of a coupled set of equations, drift-diffusion for ions and electrons, and Poisson's equation in the gas domain and cathode domain. I am having trouble enforcing boundary conditions for Poisson's equation between the gas domain and cathode. At the boundary, the potential is continuous but the electric field has a discontinuity, which is proportional to the surface charge accumulated.
Anyway, after certain simplifications,
the constraint equation is: lim_{x->-0}[a*ux+b*uxt]=lim_{x->+0}[c*ux+d*uxt] | where a,b,c,d are some constants, and, u is dependent variable, representing potential, -ux is electric field component and -uxt is the time derivate of electric field.
As you can see, since we are applying limits, the constraint is non-local. Is there a way to implement this constraint?
Dr Vardhan --please take a look at the useful links:
https://www.comsol.com/blogs/specifying-boundary-conditions-and-constraints-in-variational-problems/
https://www.comsol.com/blogs/implementing-the-weak-form-in-comsol-multiphysics/
Ijaz Durrani Thank you. The problem was resolved using linear extrusion coupling.
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