I am very new to NGSolve. I read the " Mixed formulation for second order equations" topic 2.5 Mixed formulation for second order equations — NGS-Py 6.2.2405-2-gde8f3421e documentation in the tutorial. My understanding is that it breaks down the 2nd order equation into two coupled 1st order equations. What is the benefit of doing this? Is the mixed approach more accurate? Thanks.

As stated in the beginning of the notebook, one reason is exact conservation of numerical flux. Depending if this is crucial in the application this is one way to obtain it.

Also it serves as a small model problem how this technique can be applied to solve 4th order problem without need of complicated basis functions with higher continuity, which is detailed for example here: 58. Kirchhoff plate equation — Interactive Finite Elements

Thank you for your quick reply. A follow up question is that if I implement the mixed formulation ( solving both potential phi and electrical field grad(phi) for my 2D electrostatic problem) , what would be the error estimator for adaptive meshing?