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)

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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.

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