*Article* **Numerical Method for Dirichlet Problem with Degeneration of the Solution on the Entire Boundary**

**Viktor A. Rukavishnikov \*,† and Elena I. Rukavishnikova †**

Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, Khabarovsk 680000, Russia; rukavishnikova-55@mail.ru

**\*** Correspondence: vark0102@mail.ru; Tel.: +8-421-257-2620

† These authors contributed equally to this work.

Received: 10 November 2019; Accepted: 23 November 2019; Published: 26 November 2019

**Abstract:** The finite element method (FEM) with a special graded mesh is constructed for the Dirichlet boundary value problem with degeneration of the solution on the entire boundary of the two-dimensional domain. A comparative numerical analysis is performed for the proposed method and the classical finite element method for a set of model problems in symmetric domain. Experimental confirmation of theoretical estimates of accuracy is obtained and conclusions are made.

**Keywords:** boundary value problems with degeneration of the solution on entire boundary of the domain; the method of finite elements; special graded mesh
