Analysis of a group finite element formulation

Gabriel Barrenechea, Petr Knobloch

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
70 Downloads (Pure)

Abstract

The group finite element formulation is a strategy aimed at speeding the assembly of finite element matrices for time-dependent problems. This process modifies the Galerkin matrix of the problem in a non-consistent way. This may cause a deterioration of both the stability and convergence of the method. In this paper we prove results for a group finite element formulation of a convection–diffusion–reaction equation showing that the stability of the original discrete problem remains unchanged under appropriate conditions on the data of the problem and on the discretization parameters. A violation of these conditions may lead to non-existence of solutions, as one of our main results shows. An analysis of the consistency error introduced by the group finite element formulation and its skew-symmetric variant is given.
Original languageEnglish
Pages (from-to)238-248
Number of pages11
JournalApplied Numerical Mathematics
Volume118
Early online date22 Mar 2017
DOIs
Publication statusPublished - 31 Aug 2017

Keywords

  • group finite element formulation
  • existence of solutions
  • stability
  • error estimate
  • convection-diffusion-reaction equation

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