does "generalized Neumann" boundary condition include actual Neumann boundary condition?

Question

Peter Varkonyi 2024-4-12，9:57

编辑： Torsten 2024-4-12，21:30

Hello Everyone,

I am using Matlab PDE toolbox to solve a PDE of the form

where c is a general 2 by 2 matrix, which is possibly a function of the variables.

The toolbox offers Dirichlet boundary condition or "generalized Neumann" boundary condition including boundary conditions of the from

but this does not include standard Neumann boundary condition

or other related boundary conditions

where a is a matrix different from c. Is there maybe a workaround (like change of variables) to solve these problems?

Answer 1

Torsten 2024-4-12，10:45

编辑：Torsten 2024-4-12，21:30

Is there maybe a workaround (like change of variables) to solve these problems?

No. All Neumann boundary conditions are related to the flux c*grad(u), not to grad(u) itself.