**5. Conclusions**

We can conclude according to the results of numerical experiments:

• An approximate generalized solution of Equation (1) on grids with an appropriate compression of nodes (close) to the boundary of the domain converges to an exact solution with a speed *O*(*h*2) in the norm of the space *L*2(Ω) and *O*(*h*) in the norm of the space *W*<sup>1</sup> 2,*α*(Ω) (see Tables 2 and 5);


In the next papers we plan to develop the proposed finite element method for boundary value problems with inhomogeneous boundary conditions for self-adjoint differential equations of second and higher orders with weaker conditions on the input data of the problem, in particular

*a*(*x*) ≥ −*c*, *x* ∈ Ω, *c* is finite constant.

**Author Contributions:** V.A.R. and E.I.R. contributed equally in each stage of the work. All authors read and approved the final version of the paper.

**Funding:** This research was funded by RFBR grant number 20-01-00022.

**Acknowledgments:** This research was supported in through computational resources provided by the Shared Facility Center "Data Center of FEB RAS".

**Conflicts of Interest:** The authors declare no conflict of interest.
