I am solving Poisson-like PDE with the Finite Element Method in Wolfram Mathematica. Only the Neumann boundary condition is imposed on the boundary. Of course, the solution is not unique, most likely it is unique up to a constant.

Wolfram Mathematica returns me a solution, which has enormously high absolute value, however, the solution makes sense. The problem is, at high absolute values ($\sim10^{70}$) floating point numbers have high numerical error and I cannot simply subtract this absolute value from the solution.

I there a way to make NDSolve look for solutions close to 0? Thanks in advance.