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.