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      A family of conforming mixed finite elements for linear elasticity on triangular grids

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          Abstract

          This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full \(C^0\)-\(P_k\) space enriched by \((k-1)\) \(H(\d)\) edge bubble functions on each internal edge, while the displacement field by the full discontinuous \(P_{k-1}\) vector-valued space, for the polynomial degree \(k\ge 3\). The main challenge is to find the correct stress finite element space matching the full \(C^{-1}\)-\(P_{k-1}\) displacement space. The discrete stability analysis for the inf-sup condition does not rely on the usual Fortin operator, which is difficult to construct. It is done by characterizing the divergence of local stress space which covers the \(P_{k-1}\) space of displacement orthogonal to the local rigid-motion. The well-posedness condition and the optimal a priori error estimate are proved for this family of finite elements. Numerical tests are presented to confirm the theoretical results.

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          Most cited references 22

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          Finite element interpolation of nonsmooth functions satisfying boundary conditions

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            On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers

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              A family of higher order mixed finite element methods for plane elasticity

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                Author and article information

                Journal
                2014-06-28
                2015-01-20
                Article
                1406.7457

                http://creativecommons.org/licenses/by-nc-sa/3.0/

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                Pages 17, Figures 6
                math.NA

                Numerical & Computational mathematics

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