Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776631 | Applied Numerical Mathematics | 2017 | 11 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Gabriel R. Barrenechea, Petr Knobloch,