Solving the Pure Neumann Problem by a Finite Element Method

M. I. Ivanov, I. A. Kremer, M. V. Urev

Research output: Contribution to journalArticlepeer-review


This paper deals with the solution of the pure Neumann problem for the diffusion equation by a finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analog of this problem is formulated by using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving model problems are used to discuss the numerical properties of the algorithm proposed.

Original languageEnglish
Pages (from-to)359-371
Number of pages13
JournalNumerical Analysis and Applications
Issue number4
Publication statusPublished - 1 Oct 2019


  • consistency conditions
  • finite elements
  • orthogonalization of the right-hand side
  • pure Neumann problem


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