An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes

Abstract : We present a numerical method named Mixed High Order (MHO) to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method, based on high-order local reconstructions of differential operators from face and cell degrees of freedom, exhibits a moderate computational cost thanks to hybridization and static condensation that eliminate cell unknowns. After surveying the method, we first assess its effectiveness for three-dimensional problems by comparing for the first time its performances with classical conforming finite elements. Moreover, we emphasize the algebraic equivalence of MHO in the lowest-order with the analog formulation obtained with the Discrete Geometric Approach or the Finite Integration Technique.
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IEEE Transactions on Magnetics, Institute of Electrical and Electronics Engineers, 2017, 53 (6), pp.1-4. 〈10.1109/TMAG.2017.2666546〉
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Daniele Antonio Di Pietro, Bernard Kapidani, Ruben Specogna, Francesco Trevisan. An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes. IEEE Transactions on Magnetics, Institute of Electrical and Electronics Engineers, 2017, 53 (6), pp.1-4. 〈10.1109/TMAG.2017.2666546〉. 〈hal-01399505〉

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