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A C0 Interior Penalty Finite Element Method for Flexoelectricity

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Abstract

We propose a \({\mathcal {C}}^0\) interior penalty method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as a simplified case. Standard high-order \({\mathcal {C}}^0\) finite element approximations, with nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in the interior of the elements, plus integrals on the mesh faces (sides in 2D), that impose \({\mathcal {C}}^1\) continuity of the displacement in weak form. The formulation is stable for large enough interior penalty parameter, which can be estimated solving an eigenvalue problem. The applicability and convergence of the method is demonstrated with 2D and 3D numerical examples.

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Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study. The information to reproduce the numerical results is included in the paper.

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Acknowledgements

This work was supported by the European Research Council (StG-679451 to Irene Arias), Agencia Estatal de Investigación (RTI2018-101662-B-I00), Ministerio de Economía y Competitividad (CEX2018-000797-S) and Generalitat de Catalunya (2017-SGR-1278).

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  1. Laboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, Barcelona, Spain

    Jordi Ventura, David Codony & Sonia Fernández-Méndez

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  1. Jordi Ventura
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  2. David Codony
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  3. Sonia Fernández-Méndez
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Correspondence to Sonia Fernández-Méndez.

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Ventura, J., Codony, D. & Fernández-Méndez, S. A C0 Interior Penalty Finite Element Method for Flexoelectricity. J Sci Comput 88, 88 (2021). https://doi.org/10.1007/s10915-021-01613-w

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  • DOI: https://doi.org/10.1007/s10915-021-01613-w

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