Analysis of a group finite element formulation

Barrenechea, Gabriel and Knobloch, Petr (2017) Analysis of a group finite element formulation. Applied Numerical Mathematics, 118. pp. 238-248. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2017.03.008)

[thumbnail of Barrenechea-Knobloch-ANM-2017-Analysis-of-a-group-finite-element]
Preview
 Text. Filename: Barrenechea_Knobloch_ANM_2017_Analysis_of_a_group_finite_element.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (286kB)| Preview

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.

ORCID iDs

Barrenechea, Gabriel ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Knobloch, Petr;
CORE (COnnecting REpositories)