The Brezzi-Pitkäranta stabilization scheme for the elasticity problem

In this paper, we consider the elasticity problem based on the Hellinger-Reissner variational principle. We use the equal order linear and bilinear mixed finite element spaces to approximate the stress and the displacement, and develop a Brezzi-Pitkaranta stabilization method for the finite element space pairs to overcome the lack of the inf-sup condition, then we give the error estimates of the stabilization approximation scheme. At last, we implement two numerical examples to test the stability and effectiveness of the proposed method.

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