LAUSR

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 convectiondiffusionreaction 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. The group finite element method (FEM) is analyzed for convectiondiffusionreaction equations.It is shown that the group FEM may lead to discrete problems that are not solvable.Sufficient conditions for the solvability are formulated.An alternative skew-symmetric group formulation of the convective term is presented.Consistency errors induced by the two group formulations are estimated.