### Solving a set of 5 non linear PDEs simultaneously

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Hi,

I am new to Fenics and I would like to know the best approach to solve a set of 5 non linear PDEs together. These equations are not reducible and has to be solved together. Generating the weak form manually is very difficult.

I am new to Fenics and I would like to know the best approach to solve a set of 5 non linear PDEs together. These equations are not reducible and has to be solved together. Generating the weak form manually is very difficult.

Community: FEniCS Project

### 2 Answers

2

The essence is the use of

`MixedElement`

. See nice tutorial http://www.logg.org/anders/2016/05/11/systems-of-chemical-reactions-in-fenics/
1

Based on our conversation attached to your question, I understand that the fundamental question here is how to derive the weak form given a system of PDE's in strong form.

Perhaps someone can link to a nice tutorial on this which involves FEniCS; but I learned this back when using deal.II, and this was my favorite explanation: https://www.dealii.org/8.5.0/doxygen/deal.II/group__vector__valued.html

Also to supplement the good example that Michal has already shared, here's a simple steady incompressible Navier-Stokes example which I threw together for a brief presentation to my research group: https://github.com/geo-fluid-dynamics/introduction-to-fenics/tree/master/navier-stokes

Perhaps someone can link to a nice tutorial on this which involves FEniCS; but I learned this back when using deal.II, and this was my favorite explanation: https://www.dealii.org/8.5.0/doxygen/deal.II/group__vector__valued.html

Also to supplement the good example that Michal has already shared, here's a simple steady incompressible Navier-Stokes example which I threw together for a brief presentation to my research group: https://github.com/geo-fluid-dynamics/introduction-to-fenics/tree/master/navier-stokes

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If you don't have the weak form yet, then let us know and I (unless someone beats me to it) can link you to a tutorial about deriving a weak form for a system of PDE's.