Analysis of a group finite element formulation

• ID: 2762, RIV: 10367716
• ISSN: 0168-9274, ISBN: not specified
• source: Applied Numerical Mathematics
• keywords: Group finite element formulation; Existence of solutions; Stability; Error estimates; Convection-diffusion-reaction equation
• authors: Gabriel R. Barrenechea, Petr Knobloch
• authors from KNM: Knobloch Petr

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.