Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns attached to mesh faces and cells (hence, the term hybrid), and these unknowns are polynomials of arbitrary order k ≥ 0 (hence, the term highorder). HHO methods are devised from local reconstruction operators and a local stabilization term. The discrete problem is assembled cellwise, and cell-based unknowns can be eliminated locally by static condensation. HHO methods support generalmeshes, are locally conservative, and allowfor a robust treatment of physical parameters in various situations, e.g., heterogeneous/anisotropic diffusion, quasiincompressible linear elasticity, and advection-dominated transport. This paper reviews HHO methods for a variable-diffusion model problem with nonhomogeneous, mixed Dirichlet–Neumann boundary conditions, including both primal and mixed formulations. Links with other discretization methods from the literature are discussed.
CITATION STYLE
Di Pietro, D. A., Ern, A., & Lemaire, S. (2016). A review of hybrid high-order methods: Formulations, computational aspects, comparison with other methods. In Lecture Notes in Computational Science and Engineering (Vol. 114, pp. 205–236). Springer Verlag. https://doi.org/10.1007/978-3-319-41640-3_7
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