A stabilized mixed finite element method for Poisson problem based on a three-field formulation

Abstract

We present a mixed finite element method for a three-field formulation of the Poisson problem and apply a biorthogonal system leading to an efficient numerical computation. The three-field formulation is similar to the Hu-Washizu formulation for the linear elasticity problem. A parameterised approach is given to stabilise the problem so that its associated bilinear form is coercive on the whole space. Analysis of optimal choices of parameter approximation and numerical examples are provided to evaluate our stabilised form. References

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