# Lumped matrices in thermal analysis using finite elements

The governing equation of the transient heat transfer problem is

$$C \frac{dT}{dt}+K T = Q$$

$$C$$ is the heat capacity matrix. $$K$$ is the thermal conductivity matrix. $$T$$ is the temperature vector. $$Q$$ is the heat flux vector.

I know that it is possible to use a lumped capacity matrix in thermal finite element analysis where the capacity is shifted to the nodes of every single element. Is it also possible to use lumped conductivity matrix? What will be the benefit and use case if this is possible?

No, you can't lump the $$K$$ matrix: that would not be a consistent approximation to the second-order differential operator it is supposed to represent.