Analysis of a group finite element formulation

作者：Barrenechea Gabriel R; Knobloch Petr^*

来源：Applied Numerical Mathematics, 2017, 118: 238-248.

DOI：10.1016/j.apnum.2017.03.008

• Group finite element formulation
• Existence of solutions
• Stability
• Error estimates
• Convection-diffusion-reaction equation

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.

• 出版日期2017-8