Laplace equation not provided in simulation

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The discussion revolves around a tutorial using FEMM, where the Laplace equation for the field is not explicitly provided, raising questions about its necessity. Despite the absence of the equation, the simulation appears to be functioning correctly. The tutorial emphasizes that the physics specification, including the PDE to solve, was addressed earlier in the design process. Users are encouraged to refer to the FEMM user manual for further clarification on the magnetostatic problem. Understanding the context of the simulation may alleviate concerns about the missing Laplace equation.
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I'm following this tutorial
I noticed that he provided the boundary values in FEMM but he didn't provide the Laplace equation ##\dfrac{\partial^2 V}{\partial x^2} + \dfrac{\partial^2 V}{\partial y^2} = 0## for the field but it is still corrected simulated?
or is it not necessary to provide it at all?
 
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See at 10:51ff: "The next step is to specify the physics [ie. tell it what PDE to solve]. That actually was our first step, when we created the design, we created the magnetostatic problem [at 3:26 in the first video of the series]."

The user manual for FEMM magnetics is here.
 

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