### Coupled boundary conditions

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Dear Fenics community,

I have recently been working on the implementation of the linearized Euler equations with a discontinuous Galerkin discretization in Fenics. The unknowns are the perturbations in density $\rho$

$\frac{\rho}{\rho_0}=\frac{p}{p_0}$

Where $\rho_0$

Is there a way to implement such coupled boundary conditions in Fenics? I was thinking, maybe via Lagrange multipliers?

Thank you in advance,

Max

I have recently been working on the implementation of the linearized Euler equations with a discontinuous Galerkin discretization in Fenics. The unknowns are the perturbations in density $\rho$

`ρ`, the velocity vector u and the pressure p. For an isothermal wall, the appropriate boundary condition for this kind of problem would read:$\frac{\rho}{\rho_0}=\frac{p}{p_0}$

`ρ``ρ`_{0}=`p``p`_{0}Where $\rho_0$

`ρ`_{0}and $p_0$`p`_{0}can be treated as constants for the sake of clarity. This is what I would call a coupled boundary condition, because the value of one solution variable depends on the value of another unknown solution variable.Is there a way to implement such coupled boundary conditions in Fenics? I was thinking, maybe via Lagrange multipliers?

Thank you in advance,

Max

Community: FEniCS Project

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