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 language | English |
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Pages (from-to) | 238-248 |
Number of pages | 11 |
Journal | Applied Numerical Mathematics |
Volume | 118 |
Early online date | 22 Mar 2017 |
DOIs | |
Publication status | Published - 31 Aug 2017 |
Keywords
- group finite element formulation
- existence of solutions
- stability
- error estimate
- convection-diffusion-reaction equation