Dear Community,
I am studying mixed variational problems, i.e. with multiple unknowns. When reading the exampe of the mixed poisson problem from the documentation page, I noticed that the weak forms of the two equations
\sigma -\nabla u = 0,\\
\nabla\cdot u =-f,
are then treated as one equation, by summing them:
\int \sigma\cdot \tau + \nabla\cdot \tau u + \nabla \cdot \sigma v dx = -\int fv dx + \int_\Gamma u_0 \tau\cdot n ds \qquad \forall (\tau,v)\in V\times W
I also found this old tutorial about an advection-reaction system that also sums the equations.
- How can one recover a solution from one equation, with multiple unkonwns?
- And what is the benefit of doing this versus solving a system with a “monolithic” block-matrix?
Thanks!